Title: Stability of Alexandrov-Fenchel Type Inequalities for Nearly Spherical
\n Sets in Space Forms
\nAuthors: Rong Zhou and Tailong Zhou
\nCategories: math.DG
\nComments: 25 pages
\nMSC-class: 52A40, 53C42
\n\\\\
\n In this paper, we first derive a quantitative quermassintegral inequality for
\nnearly spherical sets in $\\mathbb{H}^{n+1}$ and $\\mathbb{S}^{n+1}$, which is a
\ngeneralization of the inequality proved in $\\mathbb{R}^{n+1}$ [21]. Then we use
\nthis method to derive the stability of some geometric inequalities involving
\nweighted curvature integrals and quermassintegrals for nearly spherical sets in
\n$\\mathbb{R}^{n+1}$ and $\\mathbb{H}^{n+1}$.
\n\\\\ ( https:\/\/arxiv.org\/abs\/2306.02581 , 21kb)<\/p>\n","protected":false},"excerpt":{"rendered":"