-
作者：Thurston, Dylan P.
摘要：When is a topological branched self-cover of the sphere equivalent to a post-critically finite rational map on CP1? William Thurston gave one answer in 1982, giving a negative criterion (an obstruction to a map being rational). We give a complementary, positive criterion: the branched self-cover is equivalent to a rational map if and only if there is an elastic graph spine for the complement of the post-critical set that gets looser under backwards iteration.
-
作者：Smania, Daniel
摘要：We show that in a generic finite-dimensional real-analytic family of real-analytic multimodal maps, the subset of parameters on which the corresponding map has a solenoidal attractor with bounded combinatorics is a set with zero Lebesgue measure.
-
作者：Zhou, Xin
摘要：We prove that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves, are two-sided and have multiplicity one. This confirms a conjecture by Marques-Neves. We prove that in a bumpy metric each volume spectrum is realized by the min-max value of certain relative homotopy class of sweepouts of boundaries of Caccioppoli sets. The main result follows by approximating such...
-
作者：Maderna, Ezequiel; Venturelli, Andrea
摘要：We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h > 0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of global viscosity solutions for the Hamilton-Jacobi equation H(x, clu) = h. We prove that these solutions are fixed points of the associated Lax-Oleinik semigroup. The presented results can also be viewed as a new application of Marcha...
-
作者：Casale, Guy; Freitag, James; Nagloo, Joel
摘要：We prove the Ax-Lindemann-Weierstrass theorem with derivatives for the uniformizing functions of genus zero Fuchsian groups of the first kind. Our proof relies on differential Galois theory, monodromy of linear differential equations, the study of algebraic and Liouvillian solutions, differential algebraic work of Nishioka towards the Painleve irreducibility of certain Schwarzian equations, and considerable machinery from the model theory of differentially closed fields. Our techniques allow f...
-
作者：Alper, Jarod; Hall, Jack; Rydh, David
摘要：We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is (tale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin's algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.
-
作者：Petrow, Ian; Young, Matthew P.
摘要：We prove a Weyl-exponent subconvex bound for any Dirichlet L-function of cube-free conductor. We also show a bound of the same strength for certain L-functions of self-dual GL(2) automorphic forms that arise as twists of forms of smaller conductor.
-
作者：Judge, Chris; Mondal, Sugata
摘要：We show that a second Neumann eigenfunction u of a Euclidean triangle has at most one (non-vertex) critical point p, and if p exists, then it is a non-degenerate critical point of Morse index 1. Using this we deduce that (1) the extremal values of u are only achieved at a vertex of the triangle, and (2) a generic acute triangle has exactly one (non-vertex) critical point and that each obtuse triangle has no (non-vertex) critical points. This settles the hot spots conjecture for triangles in th...
-
作者：Branden, Petter; Huh, June
摘要：We study the class of Lorentzian polynomials. The class contains homogeneous stable polynomials as well as volume polynomials of convex bodies and projective varieties. We prove that the Hessian of a nonzero Lorentzian polynomial has exactly one positive eigenvalue at any point on the positive orthant. This property can be seen as an analog of the Hodge-Riemann relations for Lorentzian polynomials. Lorentzian polynomials are intimately connected to matroid theory and negative dependence proper...
-
作者：Angenent, Sigurd; Daskalopoulos, Panagiota; Sesum, Natasa
摘要：In this paper we consider the classification of closed non-collapsed ancient solutions to the Mean Curvature Flow (n >= 2) that are uniformly two-convex. We prove that they are either contracting spheres or they must coincide up to translations and scaling with the rotationally symmetric closed ancient non-collapsed solution first constructed by Brian White, and later by Robert Haslhofer and Or Hershkovits.
