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Stability of Alexandrov-Fenchel Type Inequalities for Nearly Spherical Sets in Space Forms
- Publication Year :
- 2023
-
Abstract
- 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 quantitative Alexandrov-Fenchel inequality proved in $\mathbb{R}^{n+1}$ [22]. 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 $\mathbb{H}^{n+1}$.<br />Comment: 24 pages
- Subjects :
- Mathematics - Differential Geometry
52A40, 53C42
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.02581
- Document Type :
- Working Paper