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arXiv · 2412.08923

Alexandrov-Fenchel type inequalities with convex weight in space forms

Kwok-Kun Kwong·Yong Wei
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Abstract

In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend classical results by incorporating weights given by convex, non-decreasing positive functions, which are otherwise arbitrary. Our approach gives rise to a broad family of geometric inequalities, as each convex, non-decreasing function yields a corresponding inequality, providing considerable flexibility.

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Kwok-Kun Kwong, Yong Wei. 2024-12-12. Alexandrov-Fenchel type inequalities with convex weight in space forms. https://doi.org/10.1007/s10231-026-01663-7

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