PreprintCC BY 4.0arXiv
The centered logarithmic Brunn--Minkowski inequality
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 Lp Brunn--Minkowski and Minkowski inequalities are also obtained for every p>0, with equality only for positive dilates, and the corresponding uniqueness of centered Lp surface area measures is established.
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BibTeX
@misc{liu2026centered,
title = {{The centered logarithmic Brunn--Minkowski inequality}},
author = {Yude Liu and Qiang Sun and Ge Xiong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10152},
eprint = {2610.10152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10152},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The centered logarithmic Brunn--Minkowski inequality
AU - Yude Liu
AU - Qiang Sun
AU - Ge Xiong
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.10152
UR - https://arxiv.org/abs/2610.10152
AB - 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.
ER -