Theoretical analysis reveals geometric rigidity of Euclidean hypersurfaces under higher order anisotropic mean curvatures, proving uniqueness of the Wulff shape up to scaling and translation.
We prove a new charcaterization of the Wulff shape in termes of higher order anisotropic mean curvatures. Namely, if a closed, connnected and oriented hypersurface of the Euclidean space has a constant higher order anisotropic mean curvature H F r and another one H F s almost constant, then it is the Wullf shape, up to translations and homotheties.
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Julien Roth (2026) studied this question.
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