Alexandrov-Fenchel type inequalities with convex weight in space forms

2024/12/12 by Kwok-Kun Kwong, Yong Wei, Kwong, Kwok-Kun +1 · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.08923

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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• On the new weighted geometric inequalities near the sphere in space forms
• New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms

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