Liberman's lemma
From HandWiki
Liberman's lemma is a theorem used in studying intrinsic geometry of convex surface. It is named after Joseph Liberman.
Formulation
If [math]\displaystyle{ \gamma }[/math] 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
- [math]\displaystyle{ t\mapsto\operatorname{dist}^2\circ\gamma(t)-t^2 }[/math]
is concave.
References
- Либерман, И. М. «Геодезические линии на выпуклых поверхностях». ДАН СССР. 32.2. (1941), 310—313.
![]() | Original source: https://en.wikipedia.org/wiki/Liberman's lemma.
Read more |