Calculus of Variations and Geometric Measure Theory
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M. Santilli

Anisotropic curvature measures and uniqueness of convex bodies

created by santilli on 05 Aug 2021

[BibTeX]

Preprint

Inserted: 5 aug 2021

Year: 2021

ArXiv: 2108.01476 PDF

Abstract:

We prove that an arbitrary convex body $C⊆\mathbf{R}^{n+1}$, whose k-th anisotropic curvature measure (for $k=0, ..., 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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