Quasigeodesics in multidimensional Alexandrov spaces
Petrunin, Anton
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https://hdl.handle.net/2142/23166
Description
Title
Quasigeodesics in multidimensional Alexandrov spaces
Author(s)
Petrunin, Anton
Issue Date
1995
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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