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.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Ricks, Russell M., "Planar CAT(k) Subspaces" (2010). All Theses and Dissertations. 2090.
CAT(k) spaces, Jordan Curve Theorem, nonpositive curvature, convexity