Liberman's lemma
Introduction '''Liberman's lemma''' is a theorem used in studying intrinsic geometry of convex surface.It is named after Joseph Liberman.
Formulation If  is a unit-speed minimizing geodesic on the surface of a convex body ''K'' in Euclidean space then for any point ''p'' ∈ ''K'', the function: is concave.
References *Либерман, И. М. «Геодезические линии на выпуклых поверхностях». ДАН СССР. 32.2. (1941), 310—313.