Abstract

Let M_k^2 be the complete, simply connected, Riemannian 2-manifold of constant curvature k ± 0. Let E be a closed, simply connected subspace of M_k^2 with the property that every two points in E are connected by a rectifi able path in E. We show that E is CAT(k) under the induced path metric.

Degree

MS

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2010-03-10

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd3420

Keywords

CAT(k) spaces, Jordan Curve Theorem, nonpositive curvature, convexity

Included in

Mathematics Commons

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