Title: Stability of Alexandrov-Fenchel Type Inequalities for Nearly Spherical
Sets in Space Forms
Authors: Rong Zhou and Tailong Zhou
Categories: math.DG
Comments: 25 pages
MSC-class: 52A40, 53C42
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In this paper, we first derive a quantitative quermassintegral inequality for
nearly spherical sets in $\mathbb{H}^{n+1}$ and $\mathbb{S}^{n+1}$, which is a
generalization of the inequality proved in $\mathbb{R}^{n+1}$ [21]. Then we use
this method to derive the stability of some geometric inequalities involving
weighted curvature integrals and quermassintegrals for nearly spherical sets in
$\mathbb{R}^{n+1}$ and $\mathbb{H}^{n+1}$.
\\ ( https://arxiv.org/abs/2306.02581 , 21kb)