Sharp Finiteness Principles For Lipschitz Selections

Charles Fefferman, Pavel Shvartsman

Research output: Contribution to journalArticle

Abstract

Let (M, ρ) be a metric space and let Y be a Banach space. Given a positive integer m, let F be a set-valued mapping from M into the family of all compact convex subsets of Y of dimension at most m. In this paper we prove a finiteness principle for the existence of a Lipschitz selection of F with the sharp value of the finiteness constant.

Original languageEnglish (US)
Pages (from-to)1641-1705
Number of pages65
JournalGeometric and Functional Analysis
Volume28
Issue number6
DOIs
StatePublished - Dec 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

Keywords

  • Helly’s theorem
  • Lipschitz selection
  • Metric tree
  • Nagata dimension
  • Set-valued mapping
  • Steiner-type point
  • Whitney partition

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