Stability of the cone-volume measure with near constant density

Abstract

We prove that if the density of the cone-volume measure of a smooth, strictly convex body with respect to the spherical Lebesgue measure is nearly constant, then a homothetic copy of the body is close to the unit ball in the $L^2$-distance.

References in corpus (3)

• Uniqueness of solutions to a class of isotropic curvature problems
• $L^p$-Minkowski Problem under Curvature Pinching
• Uniqueness of solutions to the logarithmic Minkowski problem in ${\mathbb{R}}^3$