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Criteria for farthest points on convex surfaces

✍ Scribed by Jin-ichi Itoh; Costin Vǐlcu

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
211 KB
Volume
282
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We provide a sharp, sufficient condition to decide if a point y on a convex surface S is a farthest point (i.e., is at maximal intrinsic distance from some point) on S, involving a lower bound π on the total curvature ω~y~ at y, ω~y~ ≥ π. Further consequences are obtained when ω~y~ > π, and sufficient conditions are derived to guarantee that a convex cap contains at least one farthest point. A connection between simple closed quasigeodesics O of S, points y ∈ S_O_ with ω~y~ > π, and the set 𝔽 of all farthest points on S, is also investigated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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