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Title:Extremal Problems for Curves in Metric Spaces of Curvature Bounded Above
Author(s):Maneesawarng, Chaiwat
Doctoral Committee Chair(s):Stephanie B. Alexander
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:We consider extremal problems involving curvature and curve length in metric spaces of curvature bounded above in the sense of Alexandrov. To a large extent, these problems have previously been solved only in Euclidean space. In addition to a nontrivial extention of the definition of total curvature, we give here sharp estimates of the length of a curve, one in terms of total curvature and chordlength, and another in terms of total curvature and the radius of a circumball. The latter gives rise to extremal configurations that have not previously been seen. We also establish a comparison theorem for the chordlength of a curve whose geodesic curvature is bounded by a function.
Issue Date:2000
Type:Text
Language:English
Description:104 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.
URI:http://hdl.handle.net/2142/86991
Other Identifier(s):(MiAaPQ)AAI9955650
Date Available in IDEALS:2015-09-28
Date Deposited:2000


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