| 1. |
- Xing, Yang
(author)
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Continuity of the Complex Monge-Ampere operator on compact Kahler manifolds
- 2009
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-8232 .- 1432-1823. ; 263, s. 331-344
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Journal article (peer-reviewed)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.
(author)
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Completely bounded maps and invariant subspaces
- 2020
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 1432-1823 .- 0025-5874. ; 294:1-2, s. 471-489
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Journal article (peer-reviewed)
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| 3. |
- Aleman, Alexandru, et al.
(author)
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Symmetric shift-invariant subspaces and harmonic maps
- 2021
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 299:1-2, s. 183-202
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Journal article (peer-reviewed)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.
(author)
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Fusion systems and amalgams
- 2013
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 274:3-4, s. 1119-1154
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Journal article (peer-reviewed)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
(author)
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An explicit Koppelman formula for dd(c) and Green currents on p(n)
- 2011
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 267:3-4, s. 835-850
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Journal article (peer-reviewed)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.
(author)
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Division formulas on projective varieties
- 2016
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 284:1, s. 575-593
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Journal article (peer-reviewed)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.
(author)
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On non-proper intersections and local intersection numbers
- 2022
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 300:1, s. 1019-1039
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Journal article (peer-reviewed)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
(author)
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The Collet-Eckmann condition for rational functions on the Riemann sphere
- 2013
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 273:3-4, s. 935-980
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Journal article (peer-reviewed)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.
(author)
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Bitangents of tropical plane quartic curves
- 2016
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In: Mathematische Zeitschrift. - : Springer. - 0025-5874 .- 1432-1823. ; 282:3-4, s. 1017-1031
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Journal article (peer-reviewed)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.
(author)
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Rough metrics on manifolds and quadratic estimates
- 2016
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In: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 283:3, s. 1245-1281
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Journal article (peer-reviewed)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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