Markov type of Alexandrov spaces of nonnegative curvature

Abstract

We prove that Alexandrov spaces $X$ of nonnegative curvature have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz continuous map from a subset of $X$ into a 2-uniformly convex Banach space is extended as a Lipschitz continuous map on the entire space $X$.

13 pages; v2: minor changes

References in corpus (3)

• Metric Cotype
• On metric Ramsey-type phenomena
• Hyperbolicity, CAT(-1)-spaces and the Ptolemy Inequality

Cited by in corpus (2)

• Spectral calculus and Lipschitz extension for barycentric metric spaces
• Finite flat spaces