| 1. |
- 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. - : EMS Publishing House. - 1435-9855 .- 1435-9863. ; 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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| 2. |
- 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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| 3. |
- 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. - : European Mathematical Society - EMS - Publishing House GmbH. - 1435-9855. ; 22:2, s. 477-505
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Tidskriftsartikel (refereegranskat)abstract
- The complex method of interpolation, going back to Calderon and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski 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-Ampere equation.
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| 4. |
- Boucksom, S., 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. - : European Mathematical Society - EMS - Publishing House GmbH. - 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 Kahler 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 [Der 15, 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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| 5. |
- Caraiani, A., 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. - : European Mathematical Society - EMS - Publishing House GmbH. - 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 T1.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 com-pleted homology for the same groups, analogous to conjectures of Calegari-Emerton for completed (Borel-Moore) homology.
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