-
作者：Radeschi, Marco; Wilking, Burkhard
作者单位：University of Munster
摘要：We define a Besse manifold as a Riemannian manifold (M, g) all of whose geodesics are closed. A conjecture of Berger states that all prime geodesics have the same length for any simply connected Besse manifold. We firstly show that the energy function on the free loop space of a simply connected Besse manifold is a perfect Morse-Bott function with respect to a suitable cohomology. Secondly we explain when the negative bundles along the critical manifolds are orientable. These two general resul...
-
作者：Mirzakhani, Maryam; Wright, Alex
作者单位：Stanford University
摘要：We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy.
-
作者：Shende, Vivek; Treumann, David; Zaslow, Eric
作者单位：Boston College; University of California System; University of California Berkeley; Northwestern University
摘要：We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya category of which is equivalent to the category of constructible sheaves on the surface itself. Consequently, our category can be described as constructible sheaves with singular support controlled by the front projection of the knot. We use a theorem of Guillermou-Kashiwara-Schapira to show that the resulting category is i...
-
作者：Abe, Takuro
作者单位：Kyushu University
-
作者：Potrie, Rafael; Sambarino, Andres
作者单位：Universidad de la Republica, Uruguay; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：We show that the critical exponent of a representation rho in the Hitchin component of PSL(d,R) is bounded above, the least upper bound being attained only in the Fuchsian locus. This provides a rigid inequality for the area of a minimal surface on rho\X where X is the symmetric space of PSL(d,R) The proof relies in a construction useful to prove a regularity statement: if the Frenet equivariant curve of rho is smooth, then rho is Fuchsian.
-
作者：Antonakoudis, Stergios M.
作者单位：University of Cambridge
摘要：This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichmuller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a Teichmuller disk. Additionally, a similar result is proved for a large class of disk-rigid domains, which includes strictly convex domains, as well as finite-dimensional Teichmuller spaces.
-
作者：Pulvirenti, M.; Simonella, S.
作者单位：Sapienza University Rome; University of L'Aquila; Technical University of Munich
摘要：We present a quantitative analysis of the Boltzmann-Grad (low-density) limit of a hard sphere system. We introduce and study a set of functions, the correlation errors, measuring the deviations in time from the statistical independence of particles (propagation of chaos). In the context of the BBGKY hierarchy, a correlation error of order k measures the event where k particles are connected by a chain of interactions preventing the factorization. We show that, provided , such an error flows to...
-
作者：Leble, Thomas; Serfaty, Sylvia
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Institut Universitaire de France; New York University
摘要：We study a system of N particles with logarithmic, Coulomb or Riesz pairwise interactions, confined by an external potential. We examine a microscopic quantity, the tagged empirical field, for which we prove a large deviation principle at speed N. The rate function is the sum of an entropy term, the specific relative entropy, and an energy term, the renormalized energy introduced in previous works, coupled by the temperature. We deduce a variational property of the sine-beta processes which ar...
-
作者：Chodosh, Otis; Ketover, Daniel; Maximo, Davi
作者单位：University of Cambridge; Princeton University; Stanford University; University of Pennsylvania
摘要：We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold (M-n, g), 3 <= n <= 7 can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces, up to controlled errors. Several compactness/finiteness theorems...
-
作者：Boutonnet, Remi; Ioana, Adrian; Golsefidy, Alireza Salehi
作者单位：Centre National de la Recherche Scientifique (CNRS); Inria; Universite de Bordeaux; University of California System; University of California San Diego
摘要：We introduce a novel notion of local spectral gap for general, possibly infinite, measure preserving actions. We establish local spectral gap for the left translation action , whenever is a dense subgroup generated by algebraic elements of an arbitrary connected simple Lie group G. This extends to the non-compact setting works of Bourgain and Gamburd (Invent Math 171:83-121, 2008; J Eur Math Soc (JEMS) 14:1455-1511, 2012), and Benoist and de Saxc, (Invent Math 205:337-361, 2016). We present se...
