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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License | CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives) |
Work Type | Article |
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Publication Date | December 16, 2020 |
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Deposited | January 25, 2025 |
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