Total curvature and length estimate for curves in CAT(K) spaces

Total curvature and length estimate for curves in CAT(K) spaces

We introduce the notion of total curvature of curves (which agrees with the usual one in the piecewise smooth case) in spaces of Alexandrov curvature bounded above. Basic properties of total curvature, including rectifiability of curves of finite total curvature and additivity of total curvature, ar...

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Main Authors: Chaiwat Maneesawarng, Yongwimon Lenbury
Other Authors: Mahidol University
Format: Article
Published: 2018
Subjects:
Computer Science
Mathematics
Online Access:https://repository.li.mahidol.ac.th/handle/123456789/20830
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Institution: Mahidol University
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spelling th-mahidol.208302018-07-24T10:27:37Z Total curvature and length estimate for curves in CAT(K) spaces Chaiwat Maneesawarng Yongwimon Lenbury Mahidol University Computer Science Mathematics We introduce the notion of total curvature of curves (which agrees with the usual one in the piecewise smooth case) in spaces of Alexandrov curvature bounded above. Basic properties of total curvature, including rectifiability of curves of finite total curvature and additivity of total curvature, are then obtained. A sharp upper estimate of a type due to Schmidt on the length of a curve in a CAT(K) space is also given in terms of its total curvature and the distance between its endpoints. © 2003 Elsevier B.V. All rights reserved. 2018-07-24T03:23:14Z 2018-07-24T03:23:14Z 2003-09-01 Article Differential Geometry and its Application. Vol.19, No.2 (2003), 211-222 10.1016/S0926-2245(03)00031-7 09262245 2-s2.0-0042514806 https://repository.li.mahidol.ac.th/handle/123456789/20830 Mahidol University SCOPUS https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=0042514806&origin=inward
institution Mahidol University
building Mahidol University Library
continent Asia
country Thailand
Thailand
content_provider Mahidol University Library
collection Mahidol University Institutional Repository
topic Computer Science
Mathematics
spellingShingle Computer Science
Mathematics
Chaiwat Maneesawarng
Yongwimon Lenbury
Total curvature and length estimate for curves in CAT(K) spaces
description We introduce the notion of total curvature of curves (which agrees with the usual one in the piecewise smooth case) in spaces of Alexandrov curvature bounded above. Basic properties of total curvature, including rectifiability of curves of finite total curvature and additivity of total curvature, are then obtained. A sharp upper estimate of a type due to Schmidt on the length of a curve in a CAT(K) space is also given in terms of its total curvature and the distance between its endpoints. © 2003 Elsevier B.V. All rights reserved.
author2 Mahidol University
author_facet Mahidol University
Chaiwat Maneesawarng
Yongwimon Lenbury
format Article
author Chaiwat Maneesawarng
Yongwimon Lenbury
author_sort Chaiwat Maneesawarng
title Total curvature and length estimate for curves in CAT(K) spaces
title_short Total curvature and length estimate for curves in CAT(K) spaces
title_full Total curvature and length estimate for curves in CAT(K) spaces
title_fullStr Total curvature and length estimate for curves in CAT(K) spaces
title_full_unstemmed Total curvature and length estimate for curves in CAT(K) spaces
title_sort total curvature and length estimate for curves in cat(k) spaces
publishDate 2018
url https://repository.li.mahidol.ac.th/handle/123456789/20830
_version_ 1763490077252517888

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