Short retractions of CAT(1) spaces

Abstract

We construct short retractions of a CAT(1) space to its small convex subsets. This construction provides an alternative geometric description of an analytic tool introduced by Wilfrid Kendall. Our construction uses a tractrix flow which can be defined as a gradient flow for a family of functions of certain type. In an appendix we prove a general existence result for gradient flows of time-dependent locally Lipschitz semiconcave functions, which is of independent interest.

11 pages, 2 figures. arXiv admin note: text overlap with arXiv:1903.08539

References in corpus (2)

• Area minimizing discs in metric spaces
• Area minimizing discs in locally non-compact metric spaces