Short retractions of cat(1) spaces

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.

First published in Proceedings of the American Mathematical Society on 2020-12-16, published by the American Mathematical Society. © 2020 American Mathematical Society.

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Work Title Short retractions of cat(1) spaces
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Open Access
Creators
  1. Alexander Lytchak
  2. Anton Petrunin
License CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
Work Type Article
Publisher
  1. Proceedings of the American Mathematical Society
Publication Date December 16, 2020
Publisher Identifier (DOI)
  1. https://doi.org/10.1090/proc/15268
Deposited January 25, 2025

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  • Created
  • Added 2002.09762_1_-1.pdf
  • Added Creator Alexander Lytchak
  • Added Creator Anton Petrunin
  • Published
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