Work

Logarithmic Brunn--Minkowski Inequality under $n-2$ Reflection Symmetries

Year: 2026

Type: preprint

Abstract: For origin-symmetric convex bodies in $\R^n$ invariant under $n-2$ orthogonal hyperplanes reflections, we establish the logarithmic Brunn--Minkowski inequality and classify all equality cases without regularity assumptions. We derive the logarithmic Minkowski inequality and rigidity for cone-volume measures, including an explicit classification for bodies of revolution and uniqueness for simplicial polytopes in the prescribed symmetry class.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.20730

Author: Lu, XiaoRui

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7204105657

Cites: 2

Cited by: 2

Related to: 10