Planar CAT(k) Subspaces

Details Planar CAT(k) Subspaces Planar CAT(k) Subspaces

2010-01-14

arxiv.org/abs/1001.2299v1

Mathematics

Geometric Topology

9 pages, 4 figures

Scientific paper

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

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