PreprintCC BY 4.0arXiv
Logarithmic Brunn--Minkowski Inequality under n−2 Reflection Symmetries
Abstract
For origin-symmetric convex bodies in Rn 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.
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BibTeX
@misc{lu2026logarithmic,
title = {{Logarithmic Brunn--Minkowski Inequality under $n-2$ Reflection Symmetries}},
author = {XiaoRui Lu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.20730},
eprint = {2608.20730},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20730},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Logarithmic Brunn--Minkowski Inequality under n−2 Reflection Symmetries
AU - XiaoRui Lu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2608.20730
UR - https://arxiv.org/abs/2608.20730
AB - 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.
ER -