Work

Stability of the Cone-Volume Measure With Near Constant Density

Year: 2025

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf062

Authors: Yingxiang Hu, Mohammad N Ivaki

Institutions: Beihang University, TU Wien

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

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