Universität zu Köln

Lytchak, Alexander and Petrunin, Anton ORCID: 0000-0003-3053-5172 (2021). SHORT RETRACTIONS OF CAT(1) SPACES. Proc. Amer. Math. Soc., 149 (3). S. 1247 - 1258. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6826

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lytchak, Alexander UNSPECIFIED UNSPECIFIED UNSPECIFIED Petrunin, Anton UNSPECIFIED orcid.org/0000-0003-3053-5172 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-577917
DOI:	10.1090/proc/15268
Journal or Publication Title:	Proc. Amer. Math. Soc.
Volume:	149
Number:	3
Page Range:	S. 1247 - 1258
Date:	2021
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6826
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CONVEX-FUNCTIONS; GRADIENT FLOWS; HARMONIC MAPS; CURVATURE; PURSUIT Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/57791