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Quasigeodesics in multidimensional Alexandrov spaces

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Title: Quasigeodesics in multidimensional Alexandrov spaces
Author(s): Petrunin, Anton
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Mathematics
Abstract: Here we generalize quasigeodesics to multidimensional Alexandrov space with curvature bounded from below and prove that classical theorems of Alexandrov also hold for this case. Also we develop gradient curves as a tool for studying spaces with curvature bounded from below.In the second chapter we give some applications of quasigeodesics and gradient curves: the Radius Sphere theorem, the Glueing theorem and the First variation formula for extremal subsets.
Issue Date: 1995
Type: Text
Language: English
Rights Information: Copyright 1995 Petrunin, Anton
Date Available in IDEALS: 2011-05-07
Identifier in Online Catalog: AAI9543694
OCLC Identifier: (UMI)AAI9543694

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