| 1. |
- Caraiani, Ana, et al.
(författare)
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Vanishing theorems for Shimura varieties at unipotent level
- 2023
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Ingår i: Journal of the European Mathematical Society. - 1435-9863 .- 1435-9855. ; 25:3, s. 869-911
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Tidskriftsartikel (refereegranskat)abstract
- We show that the compactly supported cohomology of Shimura varieties of Hodge type of infinite Γ1.p1/-level (defined with respect to a Borel subgroup) vanishes above the middle degree, under the assumption that the group of the Shimura datum splits at p. This generalizes and strengthens the vanishing result proved in [A. Caraiani et al., Compos. Math. 156 (2020)]. As an application of this vanishing theorem, we prove a result on the codimensions of ordinary completed homology for the same groups, analogous to conjectures of Calegari–Emerton for completed (Borel–Moore) homology.
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| 2. |
- Berndtsson, Bo, 1950, et al.
(författare)
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Complex interpolation of R-norms, duality and foliations
- 2020
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Ingår i: Journal of the European Mathematical Society. - 1435-9863 .- 1435-9855. ; 22:2, s. 477-505
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Tidskriftsartikel (refereegranskat)abstract
- The complex method of interpolation, going back to Calderón and Coifman et al., on the one hand, and the Alexander–Wermer–Słodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of interpolation of real (finite-dimensional) Banach spaces and of convex functions. The underlying duality in this method is given by the Legendre transform. Our results can also be interpreted as new properties of solutions of the homogeneous complex Monge–Ampère equation.
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| 3. |
- Boucksom, Sebastien, et al.
(författare)
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Uniform K-stability and asymptotics of energy functionals in Kähler geometry
- 2019
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Ingår i: Journal of the European Mathematical Society. - 1435-9863 .- 1435-9855. ; 21:9, s. 2905-2944
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Tidskriftsartikel (refereegranskat)abstract
- Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X, L). For many common functionals in Kähler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper [BHJ17]) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability, as defined in [Der15, BHJ17]. As a partial converse, we show that uniform K-stability implies coercivity of the Mabuchi functional when restricted to Bergman metrics.
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| 4. |
- Hytönen, Tuomas, et al.
(författare)
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Bounded variation approximation of Lp Dyadic martingales and solutions to elliptic equations
- 2018
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Ingår i: Journal of the European Mathematical Society. - 1435-9855 .- 1435-9863. ; 20:8, s. 1819-1850
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Tidskriftsartikel (refereegranskat)abstract
- We prove continuity and surjectivity of the trace map onto Lp(Rn), from a space of functions of locally bounded variation, defined by the Carleson functional. The extension map is constructed through a stopping time argument. This extends earlier work by Varopoulos in the BMO case, related to the Corona Theorem. We also prove LpCarleson approximability results for solutions to elliptic non-smooth divergence form equations, which generalize results in the case p = ∞ by Hofmann, Kenig, Mayboroda and Pipher.
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| 5. |
- Benesova, Barbora, et al.
(författare)
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A variational approach to hyperbolic evolutions and fluid-structure interactions
- 2024
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 26:12, s. 4615-4697
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Tidskriftsartikel (refereegranskat)abstract
- We show the existence of a weak solution for a system of partial differential equations describing the motion of a flexible solid inside a fluid: A nonlinear, viscoelastic, n-dimensional bulk solid governed by a PDE including inertia is interacting with an incompressible fluid governed by the (n n-dimensional) Navier-Stokes equation for n >= 2 . The result is the first allowing for large bulk deformations in the regime of long time existence for fluid-structure interactions. The existence is achieved by introducing a novel variational scheme involving two time-scales that allows us to extend the method of minimizing movements to hyperbolic problems involving nonconvex and degenerate energies.
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| 6. |
- Johansson, Anders, 1960-, et al.
(författare)
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Unique Bernoulli g-measures
- 2012
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 14:5, s. 1599-1615
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Tidskriftsartikel (refereegranskat)abstract
- We improve and subsume the conditions of Johansson and O¨ berg [18] and Berbee [2]for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular,we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely manystates under any one of the following additional assumptions.(1)P1n=1(varn log g)2 < 1,(2) For any fixed ✏ > 0,P1n=1 e−(1/2+✏)(var1 log g+···+varn log g) = 1,(3) varn log g = o(1/pn) as n!1.That the measure is Bernoulli in the case of (1) is new. In (2) we have an improved version ofBerbee’s [2] condition (concerning uniqueness and Bernoullicity), allowing the variations of log gto be essentially twice as large. Finally, (3) is an example that our main result is new both foruniqueness and for the Bernoulli property.We also conclude that we have convergence in the Wasserstein metric of the iterates of theadjoint transfer operator to the g-measure.
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| 7. |
- Ekholm, Tomas, et al.
(författare)
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Lieb-Thirring inequalities on the half-line with critical exponent
- 2008
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:3, s. 739-755
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Tidskriftsartikel (refereegranskat)abstract
- We consider the operator -d(2)/dr(2) - V in L-2(R+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound for any alpha is an element of [0, 1) and gamma >= (1 - alpha)/2. This includes a Lieb-Thirring inequality in the critical endpoint case.
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| 8. |
- Ekholm, Tobias
(författare)
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Rational symplectic field theory over Z_2 for exact Lagrangian cobordisms
- 2008
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:3, s. 641-704
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Tidskriftsartikel (refereegranskat)abstract
- We construct a version of rational symplectic field theory for pairs (X, L), where X is an exact symplectic manifold, where L ⊂ X is an exact Lagrangian submanifold with components subdivided into k subsets, and where both X and L have cylindrical ends. The theory associates to (X, L) a Z-graded chain complex of vector spaces over Z_2 , filtered with k filtration levels. The corresponding k -level spectral sequence is invariant under deformations of (X, L) and has the following property: if (X, L) is obtained by joining a negative end of a pair (X, L) to a positive end of a pair (X, L), then there are natural morphisms from the spectral sequences of (X, L) and of (X ,L) to the spectral sequence of (X, L). As an application, we show that if \Lambda ⊂ Y is a Legendrian submanifold of a contact manifold then the spectral sequences associated to (Y × R, \Lambda_s × R), where Y × R is the symplectization of Y and where \Lambda_s ⊂ Y is the Legendrian submanifold consisting of s parallel copies of \Lambda subdivided into k subsets, give Legendrian isotopy invariants of \Lambda.
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| 9. |
- Adiprasito, Karim, et al.
(författare)
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Face numbers of sequentially Cohen-Macaulay complexes and Betti numbers of componentwise linear ideals
- 2017
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 19:12, s. 3851-3865
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Tidskriftsartikel (refereegranskat)abstract
- A numerical characterization is given of the h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result determines the number of faces of various dimensions and codimensions that are possible in such a complex, generalizing the classical Macaulay-Stanley theorem to the nonpure case. Moreover, we characterize the possible Betti tables of componentwise linear ideals. A key tool in our investigation is a bijection between shifted multicomplexes of degree <= d and shifted pure. (d - 1)-dimensional simplicial complexes.
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| 10. |
- Andersen, Henning Haahr, et al.
(författare)
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Category O for quantum groups
- 2015
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 17:2, s. 405-431
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Tidskriftsartikel (refereegranskat)abstract
- We study the BGG-categories O-q associated to quantum groups. We prove that many properties of the ordinary BGG-category O for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when q is a complex root of unity. Here we prove a tensor decomposition for simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for O and for finite-dimensional U-q-modules we are able to determine all irreducible characters as well as the characters of all indecomposable tilting modules in O-q. As a consequence, we also recover the known result that the generic quantum case behaves like the classical category O.
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