Liberman's lemma - Alchetron, The Free Social Encyclopedia

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

Formulation

If γ 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

t ↦ dist 2 ∘ γ ( t ) − t 2

is concave.

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