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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
