Stability of quermassintegral inequalities along inverse curvature flows

2022/08/30 by Caroline VanBlargan, Yi Wang, VanBlargan, Caroline +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2208.14341

openalex publication_date 2022/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the stability of quermassintegral inequalities along a inverse curvature flow. We choose a special rescaling of the flow such that the k-th quermassintegral is decreasing and the k-1-th quermassintegral is preserved. Along this rescaled flow, we prove that the decreasing rate of the k-th quermassintegral is faster than the Fraenkel asymmetry of the domain when approaching to the sphere. This leads to the stability inequality of quermassintegral inequalities for nearly spherical sets using the flow method.

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• Stability of Minkowski inequality for nearly spherical sets

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