.

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 ∈ K, the function

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

is concave.

References

Liberman, J. Geodesic lines on convex surfaces. C. R. (Doklady) Acad. Sci. URSS (N.S.) 32, (1941). 310–313.

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