Premium
Criteria for farthest points on convex surfaces
Author(s) -
Itoh Jinichi,
Vǐlcu Costin
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610811
Subject(s) - mathematics , regular polygon , connection (principal bundle) , combinatorics , point (geometry) , simple (philosophy) , curvature , extreme point , convex set , geometry , mathematical analysis , convex optimization , philosophy , epistemology
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 of all farthest points on S , is also investigated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)