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arXiv · 2002.09762

Short retractions of CAT(1) spaces

Alexander Lytchak·Anton Petrunin
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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.

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Alexander Lytchak, Anton Petrunin. 2020-02-22. Short retractions of CAT(1) spaces. https://doi.org/10.1090/proc/15268

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