Stability of the Cone-Volume Measure With Near Constant Density
Abstract We prove that if the density of the cone-volume measure of a smooth, strictly convex body with respect to the spherical Lebesgue measure is nearly constant, then a homothetic copy of the body is close to the unit ball in the $L^{2}$-distance.
Authors
- Mohammad N. Ivaki (ORCID: https://orcid.org/0000-0001-7540-7268)
- Yingxiang Hu (ORCID: https://orcid.org/0000-0003-4652-7943)
Institutions
- TU Wien (AT)
- Beihang University (CN)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-03-01
- DOI
- https://doi.org/10.1093/imrn/rnaf062
- Citations
- 3
- Primary Topic
- Point processes and geometric inequalities
- Type
- article
- Field-Weighted Citation Impact
- 11.18
Funders
- National Natural Science Foundation of China
- Austrian Science Fund
- National Key Research and Development Program of China
- Fundamental Research Funds for the Central Universities