Inventiones mathematicae

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• A sharp square function estimate for the moment curve in R3 AI翻译
  作者：Maldague, Dominique
  作者单位：Massachusetts Institute of Technology (MIT)
  摘要：We prove a sharp (up to C epsilon R epsilon) L-7 square function estimate for the moment curve in R-3.
• Mean curvature flow with generic initial data AI翻译
  作者：Chodosh, Otis; Choi, Kyeongsu; Mantoulidis, Christos; Schulze, Felix
  作者单位：Stanford University; Korea Institute for Advanced Study (KIAS); Rice University; University of Warwick
  摘要：We show that the mean curvature flow of generic closed surfaces in R 3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}<^>{3}$\end{document} avoids asymptotically conical and non-spherical compact singularities. We also show that the mean curvature flow of generic closed low-entropy hypersurfaces in R 4 \d...
• Linear stability of slowly rotating Kerr black holes (vol 223, pg 1227, 2021) AI翻译
  作者：Hafner, Dietrich; Hintz, Peter; Vasy, Andras
  作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Swiss Federal Institutes of Technology Domain; ETH Zurich; Stanford University
• Uniform non-autonomous basins of attraction AI翻译
  作者：Bera, Sayani; Verma, Kaushal
  作者单位：Department of Science & Technology (India); Indian Association for the Cultivation of Science (IACS) - Jadavpur; Indian Institute of Science (IISC) - Bangalore
  摘要：It has been conjectured that every stable manifold arising from a holomorphic automorphism, that acts hyperbolically on a compact invariant set, is biholomorphic to complex Euclidean space. Such stable manifolds are known to be biholomorphic to the basin of a uniformly attracting family of holomorphic maps. It is shown that the basin of a uniformly attracting family of holomorphic maps is biholomorphic to complex Euclidean space and this resolves the conjecture on the biholomorphism type of su...
• C2-Lusin approximation of strongly convex functions AI翻译
  作者：Azagra, Daniel; Drake, Marjorie; Hajlasz, Piotr
  作者单位：Complutense University of Madrid; Massachusetts Institute of Technology (MIT); Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
  摘要：We prove that if u : R-n -> R strongly convex, then for every epsilon>0 there is a strongly convex function v is an element of C-2(Rn) such that |{u not equal v}|
• Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra AI翻译
  作者：Appel, Andrea; Toledano Laredo, Valerio
  作者单位：University of Parma; Istituto Nazionale di Fisica Nucleare (INFN); Northeastern University
  摘要：Let g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathfrak {g}$\end{document} be a symmetrisable Kac-Moody algebra and V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odd...
• Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups AI翻译
  作者：Monod, Nicolas; Nariman, Sam
  作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
  摘要：We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring generated by the bounded Euler class. These seem to be the first examples of groups for which the entire bounded cohomology can be described without being trivial. We further prove that the C-r-diffeomorphisms groups of the circle and of the c...
• Unbounded Hankel operators and the flow of the cubic Szego equation AI翻译
  作者：Gerard, Patrick; Pushnitski, Alexander
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of London; King's College London
  摘要：We prove that, for any Hankel operator with a symbol from the Hardy class H-2, the maximal and minimal domains coincide. As an application, we prove that the evolution flow of the cubic Szeg & oacute; equation on the unit circle can be continuously extended to the whole class H-2.
• Random walks, spectral gaps, and Khintchine's theorem on fractals AI翻译
  作者：Khalil, Osama; Luethi, Manuel
  作者单位：Utah System of Higher Education; University of Utah; Tel Aviv University
  摘要：This work addresses problems on simultaneous Diophantine approximation on fractals, motivated by a long standing problem of Mahler regarding Cantor's middle 1/3 set. We obtain the first instances where a complete analogue of Khintchine's Theorem holds for fractal measures. Our results apply to fractals which are self-similar by a system of rational similarities of R-d (for any d >= 1) and have sufficiently small Hausdorff co-dimension. A concrete example of such measures in the context of Mahl...
• On the conformal walk dimension: quasisymmetric uniformization for symmetric diffusions AI翻译
  作者：Kajino, Naotaka; Murugan, Mathav
  作者单位：Kobe University; Kyoto University; University of British Columbia
  摘要：We introduce the notion of conformal walk dimension, which serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that, for a given strongly local, regular symmetric Dirichlet space in which every metric ball has compact closure (MMD space), the finiteness of the conformal walk dimension characterizes the conjunction of the metric doubling property and the elliptic Harnack inequality. Roughly speaking, the conformal walk dimensi...