Liberman's lemma

Liberman's lemma is a theorem used in studying intrinsic geometry of convex surface. It is named after Joseph Liberman.

Formulation
If $$\gamma$$ is a unit-speed minimizing geodesic on the surface of a convex body K in Euclidean space then for any point p &isin; K, the function


 * $$t\mapsto\operatorname{dist}^2\circ\gamma(t)-t^2 $$

is concave.