Strongly convex set

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Template:Riemannian manifold subset property

Definition

Definition with symbols

A subset C of a Riemannian mannifold M is said to be strongly convex if given any two points p,q \in C, there is a unique normal minimal geodesic joining p with q, and moreover, this geodesic lies completely within C.

Facts

Given any point, a metric ball of sufficiently small radius about that point is strongly convex.