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Metric minimizing surfaces revisited

Anton Petrunin, Stephan Stadler

Abstract

A surface which does not admit a length nonincreasing deformation is called metric minimizing. We show that metric minimizing surfaces in CAT(0) spaces are locally CAT(0) with respect to their intrinsic metric.

Metric minimizing surfaces revisited

Abstract

A surface which does not admit a length nonincreasing deformation is called metric minimizing. We show that metric minimizing surfaces in CAT(0) spaces are locally CAT(0) with respect to their intrinsic metric.

Paper Structure

This paper contains 10 sections, 46 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Definitions
  3. Disc retracts
  4. Compactness lemma
  5. Metric-minimizing graphs
  6. Key lemma
  7. Extension lemma
  8. Proof assembling
  9. About the old theorem
  10. Saddle surfaces

Figures (2)

  • Figure :
  • Figure :