| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Proof of the cosmic no-hair conjecture in the T-3-Gowdy symmetric Einstein-Vlasov setting
- 2016
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Ingår i: Journal of the European Mathematical Society. - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9863 .- 1435-9855. ; 18:7, s. 1565-1650
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Tidskriftsartikel (refereegranskat)abstract
- The currently preferred models of the universe undergo accelerated expansion induced by dark energy. One model for dark energy is a positive cosmological constant. It is consequently of interest to study Einstein's equations with a positive cosmological constant coupled to matter satisfying the ordinary energy conditions: the dominant energy condition etc. Due to the difficulty of analysing the behaviour of solutions to Einstein's equations in general, it is common to either study situations with symmetry, or to prove stability results. In the present paper, we do both. In fact, we analyse, in detail, the future asymptotic behaviour of T-3-Gowdy symmetric solutions to the Einstein-Vlasov equations with a positive cosmological constant. In particular, we prove the cosmic no-hair conjecture in this setting. However, we also prove that the solutions are future stable (in the class of all solutions). Some of the results hold in a more general setting. In fact, we obtain conclusions concerning the causal structure of T-2-symmetric solutions, assuming only the presence of a positive cosmological constant, matter satisfying various energy conditions and future global existence. Adding the assumption of T-3-Gowdy symmetry to this list of requirements, we obtain C-0-estimates for all but one of the metric components. There is consequently reason to expect that many of the results presented in this paper can be generalised to other types of matter.
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| 6. |
- Andreasson, Håkan, 1966, et al.
(författare)
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Proof of the cosmic no-hair conjecture in the T-3-Gowdy symmetric Einstein-Vlasov setting
- 2016
-
Ingår i: Journal of the European Mathematical Society. - : EMS Publishing House. - 1435-9855 .- 1435-9863. ; 18:7, s. 1565-1650
-
Tidskriftsartikel (refereegranskat)abstract
- The currently preferred models of the universe undergo accelerated expansion induced by dark energy. One model for dark energy is a positive cosmological constant. It is consequently of interest to study Einstein's equations with a positive cosmological constant coupled to matter satisfying the ordinary energy conditions: the dominant energy condition etc. Due to the difficulty of analysing the behaviour of solutions to Einstein's equations in general, it is common to either study situations with symmetry, or to prove stability results. In the present paper, we do both. In fact, we analyse, in detail, the future asymptotic behaviour of T-3-Gowdy symmetric solutions to the Einstein-Vlasov equations with a positive cosmological constant. In particular, we prove the cosmic no-hair conjecture in this setting. However, we also prove that the solutions are future stable (in the class of all solutions). Some of the results hold in a more general setting. In fact, we obtain conclusions concerning the causal structure of T-2-symmetric solutions, assuming only the presence of a positive cosmological constant, matter satisfying various energy conditions and future global existence. Adding the assumption of T-3-Gowdy symmetry to this list of requirements, we obtain C-0-estimates for all but one of the metric components. There is consequently reason to expect that many of the results presented in this paper can be generalised to other types of matter.
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| 7. |
- Auscher, Pascal, et al.
(författare)
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L2 well-posedness of boundary value problems and the Kato square root problem for parabolic systems with measurable coefficients
- 2020
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 22:9, s. 2943-3058
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a first order strategy to study boundary value problems of parabolic systems with second order elliptic part in the upper half-space. This involves a parabolic Dirac operator at the boundary. We allow for measurable time dependence and some transversal dependence in the coefficients. We obtain layer potential representations for solutions in some classes and prove new well-posedness and perturbation results. As a byproduct, we prove for the first time a Kato estimate for the square root of parabolic operators with time dependent coefficients. This considerably extends prior results obtained by one of us under time and transversal independence. A major difficulty compared to a similar treatment of elliptic equations is the presence of non-local fractional derivatives in time.
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| 8. |
- Avelin, Benny, 1984-, et al.
(författare)
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Boundary Estimates for Certain Degenerate and Singular Parabolic Equations
- 2016
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 18:2, s. 381-424
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Tidskriftsartikel (refereegranskat)abstract
- We study the boundary behavior of non-negative solutions to a class of degenerate/singular parabolic equations, whose prototype is the parabolic p-Laplace equation. Assuming that such solutions continuously vanish on some distinguished part of the lateral part S-T of a Lipschitz cylinder, we prove Carleson-type estimates, and deduce some consequences under additional assumptions on the equation or the domain. We then prove analogous estimates for non-negative solutions to a class of degenerate/singular parabolic equations of porous medium type.
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| 9. |
- Azzam, Jonas, et al.
(författare)
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A new characterization of chord-arc domains
- 2017
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Ingår i: Journal of the European Mathematical Society (Print). - 1435-9855 .- 1435-9863. ; 19:4, s. 967-981
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Tidskriftsartikel (refereegranskat)abstract
- We show that if Ω⊂Rn+1, n≥1, is a uniform domain (also known as a 1-sided NTA domain), i.e., a domain which enjoys interior Corkscrew and Harnack Chain conditions, then uniform rectifiability of the boundary of Ω implies the existence of exterior corkscrew points at all scales, so that in fact, Ω is a chord-arc domain, i.e., a domain with an Ahlfors-David regular boundary which satisfies both interior and exterior corkscrew conditions, and an interior Harnack chain condition. We discuss some implications of this result for theorems of F. and M. Riesz type, and for certain free boundary problems.
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| 10. |
- 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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