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arXiv · 2108.01476

Anisotropic curvature measures and uniqueness of convex bodies

Mario Santilli
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Abstract

We prove that an arbitrary convex body $C \subseteq \mathbf{R}^{n+1} $, whose $ k $-th anisotropic curvature measure (for $ k =0, \ldots , n-1 $) is a multiple constant of the anisotropic perimeter of C, must be a rescaled and translated Wulff shape.This result provides a generalization of a theorem of Schneider (1979) and resolves a conjecture of Andrews and Wei (2017).

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Mario Santilli. 2022-04-14. Anisotropic curvature measures and uniqueness of convex bodies. https://arxiv.org/abs/2108.01476

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