Extremal Problems for Curves in Metric Spaces of Curvature Bounded Above

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Maneesawarng, Chaiwat

Contributors dc:contributor

• Stephanie B. Alexander

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9955650

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86991