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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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