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arXiv · 2608.15872

A nonabelian Brunn-Minkowski inequality II

Yifan Jing·Chieu-Minh Tran
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Abstract

We prove that every unimodular locally compact group $G$ of noncompact Lie dimension $n$ satisfies the sharp Brunn--Minkowski inequality \[ μ_G(XY)^{1/n}\geμ_G(X)^{1/n}+μ_G(Y)^{1/n}, \] and establish a general form for arbitrary, possibly nonunimodular, locally compact groups. This fully confirms the nonabelian Brunn--Minkowski conjecture proposed by the present authors and Zhang. As an application, we obtain an isoperimetric inequality on symmetric spaces of noncompact type.

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Yifan Jing, Chieu-Minh Tran. 2026-08-16. A nonabelian Brunn-Minkowski inequality II. https://arxiv.org/abs/2608.15872

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