| 11. |
- 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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| 12. |
- Björklund, Michael, 1981, et al.
(författare)
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Quantitative multiple mixing
- 2020
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Ingår i: Journal of the European Mathematical Society. - 1435-9863 .- 1435-9855. ; 22:5, s. 1475-1529
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Tidskriftsartikel (refereegranskat)abstract
- We develop a method for providing quantitative estimates for higher order correlations of group actions. In particular, we establish effective mixing of all orders for actions of semisimple Lie groups as well as semisimple S-algebraic groups and semisimple adele groups. As an application, we deduce existence of approximate configurations in lattices of semisimple groups.
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| 13. |
- 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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| 14. |
- Canto-Martín, Francisco, et al.
(författare)
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Perron-Frobenius operators and the Klein-Gordon equation
- 2014
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 16:1, s. 31-66
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Tidskriftsartikel (refereegranskat)abstract
- For a smooth curve Gamma and a set Lambda in the plane R-2, let AC(Gamma; Lambda) be the space of finite Borel measures in the plane supported on Gamma, absolutely continuous with respect to arc length and whose Fourier transform vanishes on Lambda. Following [12], we say that (Gamma, Lambda) is a Heisenberg uniqueness pair if AC(Gamma; Lambda) = {0}. In the context of a hyperbola Gamma, the study of Heisenberg uniqueness pairs is the same as looking for uniqueness sets Gamma of a collection of solutions to the Klein-Gordon equation. In this work, we mainly address the issue of finding the dimension of AC(Gamma; Lambda) when it is nonzero. We will fix the curve Gamma to be the hyperbola x(1)x(2) = 1, and the set Lambda = Lambda(alpha,beta) to be the lattice-cross Lambda(alpha,beta) = (alpha Zeta x {0}) boolean OR ({0} x beta Z), where alpha, beta are positive reals. We will also consider Gamma(+), the branch of x(1)x(2) = 1 where x(1) > 0. In [12], it is shown that AC(Gamma; Lambda(alpha,beta)) = {0} if and only if alpha beta <= 1. Here, we show that for alpha beta > 1, we get a rather drastic "phase transition": AC(Gamma; Lambda(alpha,beta)) is infinite-dimensional whenever alpha beta > 1. It is shown in [13] that AC(Gamma(+); Lambda(alpha,beta)) = {0} if and only if alpha beta < 4. Moreover, at the edge alpha beta = 4, the behavior is more exotic: the space AC(Gamma(+); Lambda(alpha,beta)) is one-dimensional. Here, we show that the dimension of AC(Gamma(+); Lambda(alpha,beta)) is infinite whenever alpha beta > 4. Dynamical systems, and more specifically Perron-Frobenius operators, play a prominent role in the presentation.
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| 15. |
- 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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| 16. |
- Cianchi, Andrea, et al.
(författare)
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Gradient regularity via rearrangements for p-Laplacian type elliptic boundary value problems
- 2014
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society. - 1435-9855 .- 1435-9863. ; 16:3, s. 571-595
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Tidskriftsartikel (refereegranskat)abstract
- A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.
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| 17. |
- Dolbeault, Jean, et al.
(författare)
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Lieb-Thirring inequalities with improved constants
- 2008
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 10:4, s. 1121-1126
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Tidskriftsartikel (refereegranskat)abstract
- Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrodinger operators.
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| 18. |
- Dotto, Emanuele, et al.
(författare)
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Real topological Hochschild homology
- 2021
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 23:1, s. 63-152
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Tidskriftsartikel (refereegranskat)abstract
- This paper interprets Hesselholt and Madsen's real topological Hochschild homology functor THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality and Morita invariance, and that it is suitably multiplicative. We then calculate its geometric fixed points and its Mackey functor of components, and show a decomposition result for group algebras. Using these structural results we determine the homotopy type of THR(F-p) and show that its bigraded homotopy groups are polynomial on one generator over the bigraded homotopy groups of H F-p. We then calculate the homotopy type of THR(Z) away from the prime 2, and the homotopy ring of the geometric fixed points spectrum Phi(Z/2) THR(Z).
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| 19. |
- Duits, Maurice, et al.
(författare)
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The two-periodic Aztec diamond and matrix valued orthogonal polynomials
- 2021
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855 .- 1435-9863. ; 23:4, s. 1029-1131
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Tidskriftsartikel (refereegranskat)abstract
- We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non-intersecting path model with periodic transition matrices. In a more general framework we express the correlation kernel for the underlying determinantal point process as a double contour integral that contains the reproducing kernel of matrix valued orthogonal polynomials. We use the Riemann-Hilbert problem to simplify this formula for the case of the two-periodic Aztec diamond. In the large size limit we recover the three phases of the model known as solid, liquid and gas. We describe the fine asymptotics for the gas phase and at the cusp points of the liquid-gas boundary, thereby complementing and extending results of Chhita and Johansson.
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| 20. |
- Ekholm, Tobias, 1970-, et al.
(författare)
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Legendrian knots and exact Lagrangian cobordisms
- 2016
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 18:11, s. 2627-2689
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Tidskriftsartikel (refereegranskat)abstract
- We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair (X, L) consisting of an exact symplectic manifold X and an exact Lagrangian cobordism L subset of X which agrees with cylinders over Legendrian links Lambda(+) and Lambda (-) at the positive and negative ends induces a differential graded algebra (DGA) map from the Legendrian contact homology DGA of Lambda(+) to that of Lambda (-) .We give a gradient flow tree description of the DGA maps for certain pairs (X, L), which in turn yields a purely combinatorial description of the cobordism map for elementary cobordisms, i.e., cobordisms that correspond to certain local modifications of Legendrian knots. As an application, we find exact Lagrangian surfaces that fill a fixed Legendrian link and are not isotopic through exact Lagrangian surfaces.
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