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In the differential geometry of surfaces, Liberman's lemma is key tool in studying intrinsic geometry of convex surface.

## 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.

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Liberman's_lemma — Please support Wikipedia.
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