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A Bound on the Number of Endpoints of the Cut Locus

Published online by Cambridge University Press:  01 February 2010

Robert Sinclair  and
Minoru Tanaka
Robert Sinclair
Affiliation:
Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara City, Okinawa 903–0213, Japan, [email protected], http://homepage.mac.com/r_m_sinclair/
Minoru Tanaka
Affiliation:
Department of Mathematics, Tokai University, Hiratsuka City, Kanagawa 259–1292, Japan, [email protected]

Abstract

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We provide strong experimental evidence for an upper bound on the number of endpoints of the cut locus from a point on a 2-surface of revolution. This bound is equal to the minimal number of intervals of monotone non-increasing or non-decreasing Gaussian curvature along one meridian from one pole to the other.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 9 , 2006 , pp. 21 - 39
Copyright
Copyright © London Mathematical Society 2006

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Supplementary material: File

Sinclair and Tanaka Appendix

Appendix

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