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作者：Schramm, Oded; Sheffield, Scott
作者单位：Microsoft; New York University
摘要：We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant lambda > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain-with boundary values -lambda on one boundary arc and lambda on the complementary arc-the zero level line of h joining the endpoints of these arcs converges to SLE(4) as the domain grows larger. If instead the boundary values are -a < 0 on the first arc and...
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作者：Galatius, Soren; Madsen, Ib; Tillmann, Ulrike; Weiss, Michael
作者单位：Stanford University; University of Copenhagen; University of Oxford; University of Aberdeen
摘要：The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in [S2] in order to formalize the concept of field theories. Our main result identifies the homotopy type of the classifying space of the embedded d-dimensional cobordism category for all d. For d = 2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one, presented in [MW].
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作者：Nonnenmacher, Stephane; Zworski, Maciej
作者单位：CEA; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of California System; University of California Berkeley
摘要：We study quantum scattering on manifolds equivalent to the Euclidean space near infinity, in the semiclassical regime. We assume that the corresponding classical flow admits a non-trivial trapped set, and that the dynamics on this set is of Axiom A type (uniformly hyperbolic). We are interested in the distribution of quantum resonances near the real axis. In two dimensions, we prove that, if the trapped set is sufficiently thin, then there exists a gap between the resonances and the real axis ...
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作者：Loeper, Gregoire
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We give a necessary and sufficient condition on the cost function so that the map solution of Monge's optimal transportation problem is continuous for arbitrary smooth positive data. This condition was first introduced by Ma, Trudinger and Wang [24], [30] for a priori estimates of the corresponding Monge-AmpSre equation. It is expressed by a socalled cost-sectional curvature being non-negative. We show that when the cost function is the squared distance of a Riemannian manifold, the cost-secti...
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作者：Warnaar, S. Ole
作者单位：University of Queensland
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作者：Koch, Gabriel; Nadirashvili, Nikolai; Seregin, Gregory A.; Sverak, Vladimir
作者单位：University of Chicago; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); University of Oxford; University of Minnesota System; University of Minnesota Twin Cities
摘要：We study bounded ancient solutions of the Navier-Stokes equations. These are solutions with bounded velocity defined in R (n) x (-1, 0). In two space dimensions we prove that such solutions are either constant or of the form u(x, t) = b(t), depending on the exact definition of admissible solutions. The general 3-dimensional problem seems to be out of reach of existing techniques, but partial results can be obtained in the case of axisymmetric solutions. We apply these results to some scenarios...
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作者：Fels, Gregor; Kaup, Wilhelm
作者单位：Eberhard Karls University of Tubingen
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作者：Ioana, Adrian; Peterson, Jesse
作者单位：University of California System; University of California Los Angeles
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作者：Kenig, Carlos E.; Merle, Frank
作者单位：University of Chicago; CY Cergy Paris Universite
摘要：We study the energy-critical focusing non-linear wave equation, with data in the energy space, in dimensions 3, 4 and 5. We prove that for Cauchy data of energy smaller than the one of the static solution W which gives the best constant in the Sobolev embedding, the following alternative holds. If the initial data has smaller norm in the homogeneous Sobolev space H 1 than the one of W, then we have global well-posedness and scattering. If the norm is larger than the one of W, then we have brea...
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作者：Erdos, Laszlo; Salmhofer, Manfred; Yau, Horng-Tzer
作者单位：University of Munich; Max Planck Society; Leipzig University; Harvard University
