Short retractions of cat(1) spaces

Alexander Lytchak, Anton Petrunin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1247-1257
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - Mar 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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