Tangent metric spaces to starlike sets on the plane

Details Tangent metric spaces to starlike sets on the plane Tangent metric spaces to starlike sets on the plane

2012-03-04

arxiv.org/abs/1203.0720v1

Mathematics

Metric Geometry

39 pages, 2 figures

Scientific paper

Let $A\subseteq\mathbb C$ be a starlike set with a center $a$. We prove that
every tangent space to $A$ at the point $a$ is isometric to the smallest closed
cone, with the vertex $a$, which includes $A$. A partial converse to this
result is obtained. The tangent space to convex sets is also discussed.

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