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PreprintCC BY 4.0arXiv

A centroaffine perspective on improved Brascamp--Lieb and dimensional Brunn--Minkowski inequalities

  • Sotiris Armeniakos
  • Alexander V. Kolesnikov
  • Jacopo Ulivelli
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Abstract

We study dimensional concavity properties of even log-concave measures within the framework of weighted centroaffine differential geometry. We express the relevant local concavity inequalities in terms of a weighted Hilbert--Brunn--Minkowski operator and establish an anisotropic Poincaré inequality for odd functions and a strengthened Brascamp--Lieb inequality for even functions. As applications, we obtain quantitative dimensional concavity estimates for a class of geometric measures and measures with pinched Hessian, extending results of Cordero-Erausquin and Rotem for rotationally invariant measures and Eskenazis and Moschidis for the Gaussian measure.

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Cite

BibTeXRIS
BibTeX
@misc{armeniakos2026centroaffine,
  title = {{A centroaffine perspective on improved Brascamp--Lieb and dimensional Brunn--Minkowski inequalities}},
  author = {Sotiris Armeniakos and Alexander V. Kolesnikov and Jacopo Ulivelli},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08283},
  eprint = {2611.08283},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08283},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A centroaffine perspective on improved Brascamp--Lieb and dimensional Brunn--Minkowski inequalities
AU  - Sotiris Armeniakos
AU  - Alexander V. Kolesnikov
AU  - Jacopo Ulivelli
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08283
UR  - https://arxiv.org/abs/2611.08283
AB  - We study dimensional concavity properties of even log-concave measures within the framework of weighted centroaffine differential geometry. We express the relevant local concavity inequalities in terms of a weighted Hilbert--Brunn--Minkowski operator and establish an anisotropic Poincaré inequality for odd functions and a strengthened Brascamp--Lieb inequality for even functions. As applications, we obtain quantitative dimensional concavity estimates for a class of geometric measures and measures with pinched Hessian, extending results of Cordero-Erausquin and Rotem for rotationally invariant measures and Eskenazis and Moschidis for the Gaussian measure.
ER  -