| 1. |
- Xing, Yang
(författare)
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Continuity of the Complex Monge-Ampere operator on compact Kahler manifolds
- 2009
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-8232 .- 1432-1823. ; 263, s. 331-344
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Tidskriftsartikel (refereegranskat)abstract
- We prove several approximation theorems of the complex Monge-Ampere operator on a compact Kahler manifold. As an application we prove the Cegrell type theorem on a complete description of the range of the complex Monge-Ampere operator in the class of omega-plurisubharmonic functions with vanishing complex Monge-Ampere mass on all pluripolar sets. As a by-product we obtain a stability theorem of solutions of complex Monge Ampere equations.
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| 2. |
- Alaghmandan, Mahmood, 1983, et al.
(författare)
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Completely bounded maps and invariant subspaces
- 2020
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 294:1-2, s. 471-489
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Aleman, Alexandru, et al.
(författare)
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Symmetric shift-invariant subspaces and harmonic maps
- 2021
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 299:1-2, s. 183-202
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Tidskriftsartikel (refereegranskat)abstract
- The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and k-symmetric spaces. Using an appropriate description of such symmetric shift-invariant subspaces we obtain new results for the corresponding extended solutions, including how to obtain primitive harmonic maps from certain harmonic maps into the unitary group.
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| 4. |
- Andersen, Kasper, et al.
(författare)
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Fusion systems and amalgams
- 2013
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 274:3-4, s. 1119-1154
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Tidskriftsartikel (refereegranskat)abstract
- We study reduced fusion systems from the point of view of their essential subgroups, using the classification by Goldschmidt and Fan of amalgams of prime index to analyze certain pairs of such subgroups. Our results are applied here to study reduced fusion systems over -groups of order at most 64, and also reduced fusion systems over -groups having abelian subgroups of index two. More applications are given in later papers.
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| 5. |
- Andersson, Mats, 1957
(författare)
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An explicit Koppelman formula for dd(c) and Green currents on p(n)
- 2011
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 267:3-4, s. 835-850
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Tidskriftsartikel (refereegranskat)abstract
- We compute a quite explicit Koppelman formula for dd (c) on projective space, and obtain Green currents for closed (p, p)-currents.
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| 6. |
- Andersson, Mats, 1957, et al.
(författare)
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Division formulas on projective varieties
- 2016
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 284:1, s. 575-593
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a division formula on a possibly singular projective subvariety X of complex projective space PN, which, e.g., provides explicit representations of solutions to various polynomial division problems on the affine part of X. Especially we consider a global effective version of the Briançon–Skoda–Huneke theorem. The first author was partially supported by the Swedish Research Council. The second author was supported by a postdoc grant from the Swedish Research Council.
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| 7. |
- Andersson, Mats, 1957, et al.
(författare)
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On non-proper intersections and local intersection numbers
- 2022
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 300:1, s. 1019-1039
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Tidskriftsartikel (refereegranskat)abstract
- Given equidimensional (generalized) cycles mu(1) and mu(2) on a complex manifold Y we introduce a product mu(1) lozenge Y mu(2) that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point. If Y is projective, then given a very ample line bundle L -> Y we define a product mu(1)circle L mu(2) whose multiplicities at each point also coincide with the local intersection numbers. In addition, provided that mu(1) and mu(2) are effective, this product satisfies a Bezout inequality. If i : Y -> P-N is an embedding such that i* O(1) = L, then mu(1)circle L mu(2) can be expressed as a mean value of Stuckrad-Vogel cycles on P-N. There are quite explicit relations between lozenge Y and circle L.
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| 8. |
- Aspenberg, Magnus
(författare)
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The Collet-Eckmann condition for rational functions on the Riemann sphere
- 2013
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 273:3-4, s. 935-980
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Tidskriftsartikel (refereegranskat)abstract
- We show that the set of Collet-Eckmann maps has positive Lebesgue measure in the space of rational maps on the Riemann sphere for any fixed degree d a parts per thousand yen 2.
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| 9. |
- Baker, Matthew, et al.
(författare)
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Bitangents of tropical plane quartic curves
- 2016
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Ingår i: Mathematische Zeitschrift. - : Springer. - 0025-5874 .- 1432-1823. ; 282:3-4, s. 1017-1031
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Tidskriftsartikel (refereegranskat)abstract
- We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either infinitely many or exactly 7 bitangent lines. We also prove that a smooth tropical plane quartic curve cannot be hyperelliptic.
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| 10. |
- Bandara, Lashi, 1981, et al.
(författare)
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Rough metrics on manifolds and quadratic estimates
- 2016
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 283:3, s. 1245-1281
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Tidskriftsartikel (refereegranskat)abstract
- We study the persistence of quadratic estimates related to the Kato square root problem across a change of metric on smooth manifolds by defining a class of “rough” Riemannian-like metrics that are permitted to be of low regularity and degenerate on sets of measure zero. We also demonstrate how to transmit quadratic estimates between manifolds which are homeomorphic and locally bi-Lipschitz. As a consequence, we demonstrate the invariance of the Kato square root problem under Lipschitz transformations and obtain solutions to this problem on functions and forms on compact manifolds with a rough metric. Furthermore, we show that a lower bound on the injectivity radius is not a necessary condition to solve the Kato square root problem.
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| 11. |
- Bergström, Jonas, et al.
(författare)
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On the cohomology of moduli spaces of (weighted) stable rational curves
- 2013
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 275:3-4, s. 1095-1108
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Tidskriftsartikel (refereegranskat)abstract
- We give a recursive algorithm for computing the character of the cohomology of the moduli space of stable -pointed genus zero curves as a representation of the symmetric group on letters. Using the algorithm we can show a formula for the maximum length of this character. Our main tool is connected to the moduli spaces of weighted stable curves introduced by Hassett.
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| 12. |
- Bergweiler, Walter, et al.
(författare)
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The Hausdorff dimension of Julia sets of meromorphic functions in the Speiser class
- 2022
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 302:4, s. 2193-2205
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Tidskriftsartikel (refereegranskat)abstract
- We show that for each d∈ (0 , 2] there exists a meromorphic function f such that the inverse function of f has three singularities and the Julia set of f has Hausdorff dimension d.
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| 13. |
- Berman, Robert, 1976
(författare)
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From Monge–Ampère equations to envelopes and geodesic rays in the zero temperature limit
- 2019
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 291:1-2, s. 365-394
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Tidskriftsartikel (refereegranskat)abstract
- Let (X, θ) be a compact complex manifold X equipped with a smooth (but not necessarily positive) closed (1, 1)-form θ. By a well-known envelope construction this data determines, in the case when the cohomology class [θ] is pseudoeffective, a canonical θ-psh function u θ . When the class [θ] is Kähler we introduce a family u β of regularizations of u θ , parametrized by a large positive number β, where u β is defined as the unique smooth solution of a complex Monge–Ampère equation of Aubin–Yau type. It is shown that, as β→ ∞, the functions u β converge to the envelope u θ uniformly on X in the Hölder space C 1,α (X) for any α∈] 0 , 1 [(which is optimal in terms of Hölder exponents). A generalization of this result to the case of a nef and big cohomology class is also obtained and a weaker version of the result is obtained for big cohomology classes. The proofs of the convergence results do not assume any a priori regularity of u θ . Applications to the regularization of ω-psh functions and geodesic rays in the closure of the space of Kähler metrics are given. As briefly explained there is a statistical mechanical motivation for this regularization procedure, where β appears as the inverse temperature. This point of view also leads to an interpretation of u β as a “transcendental” Bergman metric.
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| 14. |
- Berndtsson, Bo, 1950
(författare)
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Strict and nonstrict positivity of direct image bundles
- 2011
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 269:3-4, s. 1201-1218
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Tidskriftsartikel (refereegranskat)abstract
- This paper is a sequel to (Berndtsson in Ann Math 169:531-560, 2009). In that paper we studied the vector bundle associated to the direct image of the relative canonical bundle of a smooth Kahler morphism, twisted with a semipositive line bundle. We proved that the curvature of a such vector bundles is always semipositive (in the sense of Nakano). Here we address the question if the curvature is strictly positive when the Kodaira-Spencer class does not vanish. We prove that this is so provided the twisting line bundle is strictly positive along fibers, but not in general.
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| 15. |
- Björklund, Michael, 1981, et al.
(författare)
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Aperiodic order and spherical diffraction, II: translation bounded measures on homogeneous spaces
- 2021
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; In Press
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Tidskriftsartikel (refereegranskat)abstract
- We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone sets in (and even translation bounded measures on) arbitrary locally compact homogeneous metric spaces. We then specialize to the case of weighted model sets, in which we are able to derive more concrete formulas for the auto-correlation. In the case of Riemannian symmetric spaces we also explain how the auto-correlation of a weighted model set in a Riemannian symmetric space can be identified with a (typically non-tempered) positive-definite distribution on R-n. This paves the way for a diffraction theory for such model sets, which will be discussed in the sequel to the present article.
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| 16. |
- Björn, Anders
(författare)
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Removable singularities for analytic functions in BMO and locally Lipschitz spaces
- 2003
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 244:4, s. 805-835
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study removable singularities for holomorphic functions. Spaces of this type include spaces of holomorphic functions in Campanato classes, BMO and locally Lipschitz classes. Dolzhenko (1963), Král (1976) and Nguyen (1979) characterized removable singularities for some of these spaces. However, they used a different removability concept than in this paper. They assumed the functions to belong to the function space on Ω and be holomorphic on Ω \ E, whereas we only assume that the functions belong to the function space on Ω \ E, and are holomorphic there. Koskela (1993) obtained some results for our type of removability, in particular he showed the usefulness of the Minkowski dimension. Kaufman (1982) obtained some results for s=0. In this paper we obtain a number of examples with certain important properties. Similar examples have earlier been obtained for Hardy Hp classes and weighted Bergman spaces, mainly by the author. Because of the similarities in these three cases, an axiomatic approach is used to obtain some results that hold in all three cases with the same proofs.
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| 17. |
- Björn, Anders, et al.
(författare)
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Sharp Besov capacity estimates for annuli in metric spaces with doubling measures
- 2023
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Ingår i: Mathematische Zeitschrift. - : SPRINGER HEIDELBERG. - 0025-5874 .- 1432-1823. ; 305:3
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Tidskriftsartikel (refereegranskat)abstract
- We obtain precise estimates, in terms of the measure of balls, for the Besov capacity of annuli and singletons in complete metric spaces. The spaces are only assumed to be uniformly perfect with respect to the centre of the annuli and equipped with a doubling measure.
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| 18. |
- Björn, Anders, et al.
(författare)
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Sharp capacity estimates for annuli in weighted R-n and in metric spaces
- 2017
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Ingår i: Mathematische Zeitschrift. - : SPRINGER HEIDELBERG. - 0025-5874 .- 1432-1823. ; 286:3-4, s. 1173-1215
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Tidskriftsartikel (refereegranskat)abstract
- We obtain estimates for the nonlinear variational capacity of annuli in weighted R-n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R-n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R-n, which are based on quasiconformality of radial stretchings in R-n.
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| 19. |
- Björn, Anders
(författare)
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The Dirichlet problem for -harmonic functions on the topologists comb
- 2015
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Ingår i: Mathematische Zeitschrift. - : Springer Verlag (Germany). - 0025-5874 .- 1432-1823. ; 279:1-2, s. 389-405
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the Perron method for solving the -harmonic Dirichlet problem on the topologists comb. For functions which are bounded and continuous at the accessible points, we obtain invariance of the Perron solutions under arbitrary perturbations on the set of inaccessible points. We also obtain some results allowing for jumps and perturbations at a countable set of points.
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| 20. |
- Björn, Anders, et al.
(författare)
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The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy
- 2021
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Ingår i: Mathematische Zeitschrift. - : SPRINGER HEIDELBERG. - 0025-5874 .- 1432-1823. ; 297:1-2, s. 827-854
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Tidskriftsartikel (refereegranskat)abstract
- We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite pth power energy in a (not necessarily complete) metric measure space equipped with a globally doubling measure supporting a global p-Poincare inequality. The geometric conditions are that either (a) the measure has a sufficiently strong volume growth at infinity, or (b) the metric space is annularly quasiconvex (or its discrete version, annularly chainable) around some point in the space. Moreover, on the weighted real line R, we characterize all locally doubling measures, supporting a local p-Poincare inequality, for which there exist nonconstant quasiminimizers of finite p-energy, and show that a quasiminimizer is of finite p-energy if and only if it is bounded. As p-harmonic functions are quasiminimizers they are covered by these results.
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| 21. |
- Björn, Jana, 1968-, et al.
(författare)
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Orlicz capacities and Hausdorff measures on metric spaces
- 2005
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 251:1, s. 131-146
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Tidskriftsartikel (refereegranskat)abstract
- In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided that ∫10Θ -1(t1-sh(t))dt< ∞ where Θ -1 is the inverse of the function Θ(t)=Φ(t)/t, and s is the "upper dimension" of the metric measure space. This condition is a generalization of a well known condition in R n . For spaces satisfying the weaker q-Poincaré inequality, we obtain a similar but slightly more restrictive condition. Several examples are also provided. © Springer-Verlag Berlin Heidelberg 2005.
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| 22. |
- Brandes, Julia, 1986
(författare)
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On the number of linear spaces on hypersurfaces with a prescribed discriminant
- 2018
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 289:3-4, s. 803-827
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Tidskriftsartikel (refereegranskat)abstract
- For a given form we apply the circle method in order to give an asymptotic estimate of the number of m-tuples spanning a linear space on the hypersurface with the property that . This allows us in some measure to count rational linear spaces on hypersurfaces whose underlying integer lattice is primitive.
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| 23. |
- Brzezinski, Juliusz, 1939, et al.
(författare)
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Smooth lattices over quadratic integers
- 2008
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 258:1, s. 161-184
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Tidskriftsartikel (refereegranskat)abstract
- We construct lattices with quadratic structure over the integers in quadratic number fields having the property that the rank of the quadratic structure is constant and equal to the rank of the lattice in all reductions modulo maximal ideals. We characterize the case in which such lattices are free. The construction gives a representative of the genus of such lattices as an orthogonal sum of "standard" pieces of ranks 1-4 and covers the case of the discriminant of the real quadratic number field congruent to 1 modulo 8 for which a general construction was not known. © 2007 Springer-Verlag.
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| 24. |
- Bump, D., et al.
(författare)
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A local Riemann hypothesis, I
- 2000
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Ingår i: Mathematische Zeitschrift. - 0025-5874 .- 1432-1823. ; 233:1, s. 1-19
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Tidskriftsartikel (refereegranskat)
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| 25. |
- Carlini, Enrico, et al.
(författare)
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On the real rank of monomials
- 2017
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 286:1-2, s. 571-577
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the real rank of monomials and we give an upper bound for it. We show that the real and the complex ranks of a monomial coincide if and only if the least exponent is equal to one.
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