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arXiv · 2604.00562

Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds

Rongkai Zhang
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Abstract

In this paper we discuss some results regarding the rigidity of the Borell-Brascamp-Lieb inequality and the Brunn-Minkowski inequality. We show a theorem of rigidity on curvature and measure of the Borell-Brascamp-Lieb inequality, a generalisation of the curvature rigidity theorem by Balogh and Krist\'aly (Advances in Mathematics 339: 453-494, 2018, arXiv:1704.04180) to the weighted setting. We present some rigidity results of the Brunn-Minkowski inequality and a few further open problems.

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BibTeXRIS

Rongkai Zhang. 2026-04-01. Rigidity of the Borell-Brascamp-Lieb Inequality on Weighted Riemannian Manifolds. https://arxiv.org/abs/2604.00562

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