Backfitting algorithm

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

$t\mapsto {\mathrm{dist}}^2\circ \gamma (t)-t^2$

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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