2期

最新文章

• Wild ramification and spaces AI翻译
  作者：Achinger, Piotr
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Universite Paris Saclay
  摘要：We prove that every connected affine scheme of positive characteristic is a space for the ,tale topology. The main ingredient is the special case of the affine space over a field k. This is dealt with by induction on n, using a key Bertini-type statement regarding the wild ramification of -adic local systems on affine spaces, which might be of independent interest. Its proof uses in an essential way recent advances in higher ramification theory due to T. Saito. We also give rigid analytic and ...
• A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds AI翻译
  作者：Brendle, Simon; Huisken, Gerhard
  作者单位：Columbia University; Eberhard Karls University of Tubingen
  摘要：We consider a one-parameter family of closed, embedded hypersurfaces moving with normal velocity , where denote the curvature eigenvalues and is a nonnegative constant. This defines a fully nonlinear parabolic equation, provided that . In contrast to mean curvature flow, this flow preserves the condition in a general ambient manifold. Our main goal in this paper is to extend the surgery algorithm of Huisken-Sinestrari to this fully nonlinear flow. This is the first construction of this kind fo...
• Norms on the cohomology of hyperbolic 3-manifolds AI翻译
  作者：Brock, Jeffrey F.; Dunfield, Nathan M.
  作者单位：Brown University; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：We study the relationship between two norms on the first cohomology of a hyperbolic 3-manifold: the purely topological Thurston norm and the more geometric harmonic norm. Refining recent results of Bergeron, Aengun, and Venkatesh as well as older work of Kronheimer and Mrowka, we show that these norms are roughly proportional with explicit constants depending only on the volume and injectivity radius of the hyperbolic 3-manifold itself. Moreover, we give families of examples showing that some ...
• Existence of infinitely many minimal hypersurfaces in positive Ricci curvature AI翻译
  作者：Marques, Fernando C.; Neves, Andre
  作者单位：Princeton University; Imperial College London
  摘要：In the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min-max theory for the area functional to prove this conjecture in the positive Ricci curvature setting. More precisely, we show that every compact Riemannian manifold with positive Ricci curvature and dimension at most seven contains infinitely many smooth, closed, embedded minimal hypersurfaces. In the last section we mention some open pro...
• On quasi-conformal (in-) compatibility of satellite copies of the Mandelbrot set: I AI翻译
  作者：Lomonaco, Luna; Petersen, Carsten Lunde
  作者单位：Universidade de Sao Paulo; Roskilde University
  摘要：Douady and Hubbard (Ann Sci Ec Norm Suppl 4 18(2):287-343, 1985) introduced the notion of polynomial-like maps. They used it to identify homeomorphic copies of the Mandelbrot set inside the Mandelbrot set . These copies can be primitive (with a root cusp) or satellite (without a root cusp). They conjectured that the primitive copies are quasiconformally homeomorphic to , and that the satellite ones are quasiconformally homeomorphic to outside any small neighbourhood of the root. These conjectu...
• Optimal transport and Skorokhod embedding AI翻译
  作者：Beiglboeck, Mathias; Cox, Alexander M. G.; Huesmann, Martin
  作者单位：Technische Universitat Wien; University of Bath; University of Bonn
  摘要：The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a number of authors have constructed solutions with particular optimality properties. These constructions employ a variety of techniques ranging from excursion theory to potential and PDE theory and have been used in many different branches of pure and applie...
• The Noether-Lefschetz conjecture and generalizations AI翻译
  作者：Bergeron, Nicolas; Li, Zhiyuan; Millson, John; Moeglin, Colette
  作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Fudan University; University System of Maryland; University of Maryland College Park; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
  摘要：We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes of arithmetic manifolds of orthogonal type are dual to the classes of special cycles, i.e. sub-arithmetic manifolds of the same type. For compact manifolds this was proved in [3], here we extend the results of [3] to non-compact manifolds. This allows us to apply our results to the moduli spaces of...
• Existence h-principle for Engel structures AI翻译
  作者：Casals, Roger; Luis Perez, Jose; del Pino, Alvaro; Presas, Francisco
  作者单位：Massachusetts Institute of Technology (MIT); Autonomous University of Madrid; Universidad Carlos III de Madrid; Complutense University of Madrid; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencias Matematicas (ICMAT); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM)
  摘要：In this article we prove that the inclusion of the space of Engel structures of a smooth 4-manifold into the space of full flags of its tangent bundle induces surjections in all homotopy groups. In particular, we construct Engel structures representing any given full flag.
• New explicit formulas for Faltings' delta-invariant AI翻译
  作者：Wilms, Robert
  作者单位：Johannes Gutenberg University of Mainz
  摘要：In this paper we give new explicit formulas for Faltings' -invariant in terms of integrals of theta functions, and we deduce an explicit lower bound for only in terms of the genus and an explicit upper bound for the Arakelov-Green function in terms of . Furthermore, we give a canonical extension of and the Zhang-Kawazumi invariant to the moduli space of indecomposable principally polarised complex abelian varieties.
• Prime values of a2 + p4 AI翻译
  作者：Heath-Brown, D. R.; Li, Xiannan
  作者单位：University of Oxford
  摘要：We prove an asymptotic formula for the number of primes of the shape , thereby refining the well known work of Friedlander and Iwaniec (Ann Math (2) 148(3):945-1040, 1998). Along the way, we prove a result on equidistribution of primes up to x, in which the moduli may be almost as large as x(2).