Tangent metric spaces to starlike sets on the plane

Abstract

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.

39 pages, 2 figures