Year: 2026
Type: preprint
Abstract: The logarithmic Brunn--Minkowski and logarithmic Minkowski inequalities are proved for convex bodies whose centroids are at the origin, with equality precisely for independent positive dilations of common direct summands. This characterizes when centered convex bodies have the same cone-volume measure. The \(L_p\) Brunn--Minkowski and Minkowski inequalities are also obtained for every \(p>0\), with equality only for positive dilates, and the corresponding uniqueness of centered \(L_p\) surface area measures is established.
Source: arXiv (Cornell University)
Authors: Liu, Yude, Sun, Qiang, Xiong, Ge
Institutions: Fudan University, Tongji University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220927193