Remarks on Manifolds with Two-Sided Curvature Bounds

We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.

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Main Authors:	Kapovitch Vitali, Lytchak Alexander
Format:	article
Language:	EN
Published:	De Gruyter 2021
Subjects:	distance functions cut locus subsets of positive reach harmonic coordinates alexandrov spaces 53c20 53c21 53c23 Analysis QA299.6-433
Online Access:	https://doaj.org/article/3155ae78093a4e5da12006a0eb37260d
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spelling	oai:doaj.org-article:3155ae78093a4e5da12006a0eb37260d2021-12-05T14:10:38ZRemarks on Manifolds with Two-Sided Curvature Bounds2299-327410.1515/agms-2020-0122https://doaj.org/article/3155ae78093a4e5da12006a0eb37260d2021-06-01T00:00:00Zhttps://doi.org/10.1515/agms-2020-0122https://doaj.org/toc/2299-3274We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.Kapovitch VitaliLytchak AlexanderDe Gruyterarticledistance functionscut locussubsets of positive reachharmonic coordinatesalexandrov spaces53c2053c2153c23AnalysisQA299.6-433ENAnalysis and Geometry in Metric Spaces, Vol 9, Iss 1, Pp 53-64 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	distance functions cut locus subsets of positive reach harmonic coordinates alexandrov spaces 53c20 53c21 53c23 Analysis QA299.6-433
spellingShingle	distance functions cut locus subsets of positive reach harmonic coordinates alexandrov spaces 53c20 53c21 53c23 Analysis QA299.6-433 Kapovitch Vitali Lytchak Alexander Remarks on Manifolds with Two-Sided Curvature Bounds
description	We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.
format	article
author	Kapovitch Vitali Lytchak Alexander
author_facet	Kapovitch Vitali Lytchak Alexander
author_sort	Kapovitch Vitali
title	Remarks on Manifolds with Two-Sided Curvature Bounds
title_short	Remarks on Manifolds with Two-Sided Curvature Bounds
title_full	Remarks on Manifolds with Two-Sided Curvature Bounds
title_fullStr	Remarks on Manifolds with Two-Sided Curvature Bounds
title_full_unstemmed	Remarks on Manifolds with Two-Sided Curvature Bounds
title_sort	remarks on manifolds with two-sided curvature bounds
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/3155ae78093a4e5da12006a0eb37260d
work_keys_str_mv	AT kapovitchvitali remarksonmanifoldswithtwosidedcurvaturebounds AT lytchakalexander remarksonmanifoldswithtwosidedcurvaturebounds
_version_	1718371891200131072

Remarks on Manifolds with Two-Sided Curvature Bounds

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