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Alexandrov meets Kirszbraun

Stephanie Alexander, Vitali Kapovitch, Anton Petrunin

Abstract

We give a simplified proof of the generalized Kirszbraun theorem for Alexandrov spaces, which is due to Lang and Schroeder. We also discuss related questions, both solved and open.

Alexandrov meets Kirszbraun

Abstract

We give a simplified proof of the generalized Kirszbraun theorem for Alexandrov spaces, which is due to Lang and Schroeder. We also discuss related questions, both solved and open.

Paper Structure

This paper contains 9 sections, 70 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Short map extension definitions.
  4. (1+n)-point comparison
  5. Kirszbraun's theorem
  6. (2n+2)-point comparison
  7. Comments and open problems
  8. Barycentric simplex
  9. Helly's theorem