Inventiones mathematicae

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• On the Cauchy problem for gravity water waves AI翻译
  作者：Alazard, T.; Burq, N.; Zuily, C.
  作者单位：Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
  摘要：We are interested in the system of gravity water waves equations without surface tension. Our purpose is to study the optimal regularity thresholds for the initial conditions. In terms of Sobolev embeddings, the initial surfaces we consider turn out to be only of -class for some and consequently have unbounded curvature, while the initial velocities are only Lipschitz. We reduce the system using a paradifferential approach.
• Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space (vol 180, pg 559, 2010) AI翻译
  作者：Bauer, I.; Catanese, F.
  作者单位：University of Bayreuth
• Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions AI翻译
  作者：Jia, Hao; Sverak, Vladimir
  作者单位：University of Minnesota System; University of Minnesota Twin Cities
  摘要：We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with (-1)-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.
• On special zeros of p-adic L-functions of Hilbert modular forms AI翻译
  作者：Spiess, Michael
  作者单位：University of Bielefeld
  摘要：Let E be a modular elliptic curve over a totally real number field F. We prove the weak exceptional zero conjecture which links a (higher) derivative of the p-adic L-function attached to E to certain p-adic periods attached to the corresponding Hilbert modular form at the places above p where E has split multiplicative reduction. Under some mild restrictions on p and the conductor of E we deduce the exceptional zero conjecture in the strong form (i.e. where the automorphic p-adic periods are r...
• Maximal modifications and Auslander-Reiten duality for non-isolated singularities AI翻译
  作者：Iyama, Osamu; Wemyss, Michael
  作者单位：Nagoya University; University of Edinburgh; Heriot Watt University
  摘要：We first generalize classical Auslander-Reiten duality for isolated singularities to cover singularities with a one-dimensional singular locus. We then define the notion of CT modules for non-isolated singularities and we show that these are intimately related to noncommutative crepant resolutions (NCCRs). When R has isolated singularities, CT modules recover the classical notion of cluster tilting modules but in general the two concepts differ. Then, wanting to generalize the notion of NCCRs ...
• On the connectivity of the Julia sets of meromorphic functions AI翻译
  作者：Baranski, Krzysztof; Fagella, Nuria; Jarque, Xavier; Karpinska, Boguslawa
  作者单位：University of Warsaw; University of Barcelona; Warsaw University of Technology
  摘要：We prove that every transcendental meromorphic map f with disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions, whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton...
• Group cohomology and control of p-fusion AI翻译
  作者：Benson, David J.; Grodal, Jesper; Henke, Ellen
  作者单位：University of Aberdeen; University of Copenhagen
  摘要：We show that if an inclusion of finite groups Ha parts per thousand currency signG of index prime to p induces a homeomorphism of mod p cohomology varieties, or equivalently an F-isomorphism in mod p cohomology, then H controls p-fusion in G, if p is odd. This generalizes classical results of Quillen who proved this when H is a Sylow p-subgroup, and furthermore implies a hitherto difficult result of Mislin about cohomology isomorphisms. For p=2 we give analogous results, at the cost of replaci...
• On the local-global conjecture for integral Apollonian gaskets With an appendix by Peter P. Varju AI翻译
  作者：Bourgain, Jean; Kontorovich, Alex
  作者单位：Institute for Advanced Study - USA; Yale University
  摘要：We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) admissible (passing local obstructions) integer is the curvature of some circle in the gasket.
• The Iwasawa Main Conjectures for GL2 AI翻译
  作者：Skinner, Christopher; Urban, Eric
  作者单位：Princeton University; Sorbonne Universite; Universite Paris Cite; Columbia University
  摘要：We prove the one-, two-, and three-variable Iwasawa-Greenberg Main Conjectures for a large class of modular forms that are ordinary with respect to an odd prime p. The method of proof involves an analysis of an Eisenstein ideal for ordinary Hida families for GU(2,2).
• Joint quasimodes, positive entropy, and quantum unique ergodicity AI翻译
  作者：Brooks, Shimon; Lindenstrauss, Elon
  作者单位：Bar Ilan University; Hebrew University of Jerusalem
  摘要：We study joint quasimodes of the Laplacian and one Hecke operator on compact congruence surfaces, and give conditions on the orders of the quasimodes that guarantee positive entropy on almost every ergodic component of the corresponding semiclassical measures. Together with the measure classification result of (Lindenstrauss, Ann Math (2) 163(1):165-219, 2006), this implies Quantum Unique Ergodicity for such functions. Our result is optimal with respect to the dimension of the space from which...