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arxiv: 2606.22847 · v1 · pith:776VFH36new · submitted 2026-06-22 · 🧮 math.AP

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

Jiahuan Li , Xi-Nan Ma , Paolo Salani This is my paper
classification 🧮 math.AP
keywords convexdomainhessianboundedbrunn--minkowskieigenvalueinequalitymathbb
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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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  1. Brunn--Minkowski Inequality for the First Complex $\sigma_{2}$-Hessian Eigenvalue

    math.AP 2026-06 unverdicted novelty 6.0

    Proves strict real log-concavity of the first eigenfunction of the complex σ₂-Hessian operator on real uniformly strictly convex domains in ℂ^n and derives the corresponding Brunn-Minkowski inequality for its eigenvalue.