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October 15, 2025Open Access

On p-Brunn-Minkowski and Brascamp-Lieb inequalities

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Authors

AKAlexander V. KolesnikovGLGalyna V. LivshytsLRLiran Rotem

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Overview

This paper reveals links between Brascamp-Lieb and p-Brunn-Minkowski inequalities, suggesting new conditions for symmetric log-concave measures.

Key Points

  • A strong version of the Brascamp-Lieb inequality is equivalent to a p-Brunn-Minkowski inequality.
  • New sufficient conditions for symmetric p-Brunn-Minkowski inequality are established with p < 1.
  • Local log-Brunn-Minkowski inequality for L_q-balls is proven for all dimensions and q ≥ 1.
  • This is a significant extension from previous results which were limited to q ≥ 2.

Cite This Study

Kolesnikov et al. (2025) studied this question.

synapsesocial.com/papers/68ef858cc6a308ba06355512https://doi.org/10.48550/arxiv.2507.12099
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