https://arxiv.org/abs/2002.09762 [Submitted on 22 Feb 2020]
Short retractions of CAT(1) spaces
Alexander Lytchak, Anton Petrunin
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.