Barycentric gluing and geometry of stable metrics View Full Text


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Article Info

DATE

2021-11-09

AUTHORS

F. P. Baudier

ABSTRACT

We discuss various aspects of a local-to-global embedding technique and the metric geometry of stable metric spaces, in particular two of its important subclasses: locally finite spaces and proper spaces. We explain how the barycentric gluing technique, which has been mostly applied to bi-Lipschitz embedding problems pertaining to locally finite spaces, can be implemented successfully in a much broader context. For instance, we show that the embeddability of an arbitrary metric space into ℓp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _p$$\end{document} is determined by the embeddability of its balls. We also introduce the notion of upper stability. This new metric invariant lies formally between Krivine–Maurey (isometric) notion of stability and Kalton’s property Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {Q}}$$\end{document}. We show that several results of Raynaud and Kalton for stable metrics can be extended to the broader context of upper stable metrics and we point out the relevance of upper stability to a long standing embedding problem raised by Kalton. Applications to compression exponent theory are highlighted and we recall old, and state new, important open problems. This article was written in a style favoring clarity over conciseness in order to make the material appealing, accessible, and reusable to geometers from a variety of backgrounds, and not only to Banach space geometers. More... »

PAGES

37

References to SciGraph publications

  • 2013-04-09. Nonlinear spectral calculus and super-expanders in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 1984-06. Existence of separable uniformly homeomorphic nonisomorphic Banach spaces in ISRAEL JOURNAL OF MATHEMATICS
  • 1981-09. Quelques proprietes des espaces de Banach stables in ISRAEL JOURNAL OF MATHEMATICS
  • 2000-01-01. The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space in INVENTIONES MATHEMATICAE
  • 1982. Stable Banach spaces, random measures and Orlicz function spaces in PROBABILITY MEASURES ON GROUPS
  • 2019-04-06. Nonpositive curvature is not coarsely universal in INVENTIONES MATHEMATICAE
  • 2008-12-17. Trees and Markov Convexity in GEOMETRIC AND FUNCTIONAL ANALYSIS
  • 1974-09. Every separable metric space is Lipschitz equivalent to a subset ofc0+ in ISRAEL JOURNAL OF MATHEMATICS
  • 1987. Random series in the real interpolation spaces between the spaces vp in GEOMETRICAL ASPECTS OF FUNCTIONAL ANALYSIS
  • 2019-04-30. Coarse embeddings into superstable spaces in ISRAEL JOURNAL OF MATHEMATICS
  • 1981-12. Espaces de Banach stables in ISRAEL JOURNAL OF MATHEMATICS
  • 2007-12-01. The coarse Lipschitz geometry of in MATHEMATISCHE ANNALEN
  • 2010. Spaces and Questions in VISIONS IN MATHEMATICS
  • 1974-04. Not every Banach space contains an imbedding oflp or c0 in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 1983-03. Espaces de Banach superstables, distances stables et homeomorphismes uniformes in ISRAEL JOURNAL OF MATHEMATICS
  • 1910-06. Les dimensions d'un ensemble abstrait in MATHEMATISCHE ANNALEN
  • 1986-06. The metrical interpretation of superreflexivity in banach spaces in ISRAEL JOURNAL OF MATHEMATICS
  • 2002. Lectures on Discrete Geometry in NONE
  • 1978-03. Nonreflexive spaces of type 2 in ISRAEL JOURNAL OF MATHEMATICS
  • 2007-10-19. Metrical characterization of super-reflexivity and linear type of Banach spaces in ARCHIV DER MATHEMATIK
  • 2012-11-17. An introduction to the Ribe program in JAPANESE JOURNAL OF MATHEMATICS
  • 1970-08. On a problem of Smirnov in ARKIV FÖR MATEMATIK
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