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arXiv · 2606.22847

A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain

Jiahuan Li·Xi-Nan Ma·Paolo Salani
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Abstract

We use the deformation methods to obtain the strictly log concavity of solution of a class Hessian equation in bounded convex domain in $\mathbb{R}^{n}$, as an application we get the Brunn--Minkowski inequality for the Hessian eigenvalue and characterize the equality case in bounded strictly convex domain in $\mathbb{R}^{n}$.

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Jiahuan Li, Xi-Nan Ma, Paolo Salani. 2026-06-22. A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain. https://arxiv.org/abs/2606.22847

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