# Strongly convex set

From Diffgeom

Template:Riemannian manifold subset property

## Definition

### Definition with symbols

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

## Facts

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