-
作者：Lenzmann, Enno; Schikorra, Armin
作者单位：University of Basel; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We consider the energy-critical half-wave maps equation . We give a complete classification of all traveling solitary waves with finite energy. The proof is based on a geometric characterization of these solutions as minimal surfaces with (not necessarily free) boundary on . In particular, we discover an explicit Lorentz boost symmetry, which is implemented by the conformal Mobius group on the target applied to half-harmonic maps from to . Complementing our classification result, we carry out ...
-
作者：Jaffard, Stephane; Martin, Bruno
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite du Littoral-Cote-d'Opale
摘要：The Brjuno function B is a 1-periodic, nowhere locally bounded function, introduced by Yoccoz because it encapsulates a key information concerning analytic small divisor problems in dimension 1. We show that regularity, introduced by Caldern and Zygmund, is the only one which is relevant in order to unfold the pointwise regularity properties of B; we determine its regularity at every point and show that it is directly related to the irrationality exponent : its p-exponent at x is exactly . Thi...
-
作者：Cieliebak, K.; Mohnke, K.
作者单位：University of Augsburg; Humboldt University of Berlin
摘要：We use a neck stretching argument for holomorphic curves to produce symplectic disks of small area and Maslov class with boundary on Lagrangian submanifolds of nonpositive curvature. Applications include the proof of Audin's conjecture on the Maslov class of Lagrangian tori in linear symplectic space, the construction of a new symplectic capacity, obstructions to Lagrangian embeddings into uniruled symplectic manifolds, a quantitative version of Arnold's chord conjecture, and estimates on the ...
-
作者：Balla, Igor; Draxler, Felix; Keevash, Peter; Sudakov, Benny
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oxford
摘要：A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R-n was extensively studied for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, in this paper we prove that for every fixed angle theta and sufficiently large there are at most 2n-2 lines in R-n with common angle theta. Moreover, this bound is achieved if and only if theta = a...
