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

Issued Date

2003-09-01

Resource Type

Article

ISSN

09262245

DOI

10.1016/S0926-2245(03)00031-7

Other identifier(s)

2-s2.0-0042514806

Rights

Mahidol University

Rights Holder(s)

SCOPUS

Bibliographic Citation

Differential Geometry and its Application. Vol.19, No.2 (2003), 211-222

Suggested Citation

Chaiwat Maneesawarng, Yongwimon Lenbury Total curvature and length estimate for curves in CAT(K) spaces. Differential Geometry and its Application. Vol.19, No.2 (2003), 211-222. doi:10.1016/S0926-2245(03)00031-7 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/20830

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Title

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

Author(s)

Chaiwat Maneesawarng
 Yongwimon Lenbury

Other Contributor(s)

Mahidol University

Abstract

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.

Keyword(s)

Computer Science
 Mathematics

Availability

URI

https://repository.li.mahidol.ac.th/handle/20.500.14594/20830

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Scopus 2001-2005