A note on new weighted geometric inequalities for hypersurfaces in \mathbb Rⁿ

2023/11/27 by Jie Wu, Wu, Jie
Mathematics · #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2311.15794

openalex publication_date 2023/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we prove a family of sharp weighed inequality which involves weighted k-th mean curvature integral and two distinct quermassintegrals for closed hypersurfaces in ℝⁿ. This inequality generalizes the corresponding result of Wei and Zhou \citeWZ where their proof is based on earlier results of Kwong-Miao \citeKM1,KM2. Here we present a proof which does not rely on Kwong-Miao's results.

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