Blaschke-Type Theorem and Separation of Disjoint Closed Geodesic Convex Sets

Abstract

In this paper, we deal with analytic and geometrical properties of geodesic convex sets and geodesic paths. We show that Blaschke’s Theorem for convex sets is also true for geodesic convex sets and geodesic paths in a simple polygon. Some geometrical properties of geodesic triangles are presented. Furthermore, separation of geodesic convex sets is shown.