Liberman's lemma

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.

gollark: The split in what?

gollark: I don't think this substantively addresses what I said.

gollark: It seems that you explicitly suggested it was good because it gave more power to rural people than they would otherwise get based on population.

gollark: According to my badness determination metrics.

gollark: What I am saying is that deliberately designing an electoral system and then messing with it so that a particular group consistently gets outsized amounts of power is bad, and that it isn't particularly justified based on "cultural differences" because there are lots of culturally different groups.

References

Либерман, И. М. «Геодезические линии на выпуклых поверхностях». ДАН СССР. 32.2. (1941), 310—313.

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