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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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 |
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Computer Science Mathematics Chaiwat Maneesawarng Yongwimon Lenbury Total curvature and length estimate for curves in CAT(K) spaces |
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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. |
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Mahidol University |
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Mahidol University Chaiwat Maneesawarng Yongwimon Lenbury |
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Article |
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Chaiwat Maneesawarng Yongwimon Lenbury |
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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 |
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Total curvature and length estimate for curves in CAT(K) spaces |
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total curvature and length estimate for curves in cat(k) spaces |
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2018 |
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https://repository.li.mahidol.ac.th/handle/123456789/20830 |
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