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Antipodal trees and mutually critical points on surfaces
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Tudor Zamfirescu
Published/Copyright:
June 28, 2007
Abstract
To any point on an Alexandrov surface homeomorphic to the sphere one can associate a minimal subtree of the cut locus containing all farthest points. It is called the antipodal tree.
Two points of a compact orientable Alexandrov surface are called mutually critical if each of them is critical with respect to the other. All points which are mutually critical with a given point form a set. In this paper we show that this set, as well as the set of endpoints of any antipodal tree, are finite.
Received: 2005-10-21
Revised: 2006-02-24
Published Online: 2007-06-28
Published in Print: 2007-07-20
© Walter de Gruyter
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with nonzero constant mean curvature - On a 25-dimensional embedding of the Ree–Tits generalized octagon
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