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作者：Jendrej, Jacek; Lawrie, Andrew
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13; Massachusetts Institute of Technology (MIT)
摘要：We consider the energy-critical wave maps equation in the equivariant case, with equivariance degree . It is known that initial data of energy and topological degree zero leads to global solutions that scatter in both time directions. We consider the threshold case of energy . We prove that the solution is defined for all time and either scatters in both time directions, or converges to a superposition of two harmonic maps in one time direction and scatters in the other time direction. In the ...
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作者：Bao, Huanchen; Wang, Weiqiang
作者单位：University System of Maryland; University of Maryland College Park; University of Virginia
摘要：We develop a general theory of canonical bases for quantum symmetric pairs with parameters of arbitrary finite type. We construct new canonical bases for the finite-dimensional simple -modules and their tensor products regarded as -modules. We also construct a canonical basis for the modified form of the quantum group . To that end, we establish several new structural results on quantum symmetric pairs, such as bilinear forms, braid group actions, integral forms, Levi subalgebras (of real rank...
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作者：Petridis, Yiannis N.; Risager, Morten S.
作者单位：University of London; University College London; University of Copenhagen
摘要：Mazur, Rubin, and Stein have recently formulated a series of conjectures about statistical properties of modular symbols in order to understand central values of twists of elliptic curve L-functions. Two of these conjectures relate to the asymptotic growth of the first and second moments of the modular symbols. We prove these on average by using analytic properties of Eisenstein series twisted by modular symbols. Another of their conjectures predicts the Gaussian distribution of normalized mod...
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作者：Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Gunther
作者单位：University of London; University College London; University of Helsinki; University of Washington; University of Washington Seattle
摘要：We study two inverse problems on a globally hyperbolic Lorentzian manifold (M, g). The problems are: Passive observations in spacetime: consider observations in an open set . The light observation set corresponding to a point source at is the intersection of V and the light-cone emanating from the point q. Let be an unknown open, relatively compact set. We show that under natural causality conditions, the family of light observation sets corresponding to point sources at points determine uniqu...
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作者：Ma, Shouhei
作者单位：Institute of Science Tokyo; Tokyo Institute of Technology
摘要：We prove that up to scaling there are only finitely many integral lattices L of signature (2, n) with or such that the modular variety defined by the orthogonal group of L is not of general type. In particular, when , every modular variety defined by an arithmetic group for a rational quadratic form of signature (2, n) is of general type. We also obtain similar finiteness in for the stable orthogonal groups. As a byproduct we derive finiteness of lattices admitting reflective modular form of b...
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作者：Liero, Matthias; Mielke, Alexander; Savare, Giuseppe
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Pavia
摘要：We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. These problems arise quite naturally by relaxing the marginal constraints typical of Optimal Transport problems: given a pair of finite measures (with possibly different total mass), one looks for minimizers of the sum of a linear transport functional and two convex entropy functionals, which quantify in some way the deviation of the marg...
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作者：Hadzic, Mahir; Jang, Juhi
作者单位：University of Southern California; Korea Institute for Advanced Study (KIAS)
摘要：Without any symmetry assumptions on the initial data we construct global-in-time unique solutions to the vacuum free boundary three-dimensional isentropic compressible Euler equations when the adiabatic exponent. lies in the interval (1, 53]. Our initial data lie sufficiently close to the expanding compactly supported affine motions recently constructed by Sideris and they satisfy the physical vacuum boundary condition.
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作者：Ginzburg, Viktor L.; Gurel, Basak Z.
作者单位：State University System of Florida; University of Central Florida; University of California System; University of California Santa Cruz
摘要：Themain theme of the paper is the dynamics of Hamiltonian diffeomorphisms of CPn with theminimal possible number of periodic points (equal to n + 1 by Arnold's conjecture), called here Hamiltonian pseudo-rotations. We prove several results on the dynamics of pseudo-rotations going beyond periodic orbits, using Floer theoretical methods. One of these results is the existence of invariant sets in arbitrarily small punctured neighborhoods of the fixed points, partially extending a theorem of Le C...
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作者：Martel, Yvan; Merle, Frank
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Institut Polytechnique de Paris; Ecole Polytechnique; CY Cergy Paris Universite; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：For the focusing energy critical wave equation in 5D, we construct a solution showing the inelastic nature of the collision of two solitons for any choice of sign, speed, scaling and translation parameters, except the special case of two solitons of same scaling and opposite signs. Beyond its own interest as one of the first rigorous studies of the collision of solitons for a non-integrable model, the case of the quartic gKdV equation being partially treated in Martel and Merle (Ann Math 174(2...
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作者：Loray, Frank; Pereira, Jorge Vitorio; Touzet, Frederic
作者单位：Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds.
