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.
A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain
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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 $\mathbb{R}^{n}$.
fields
math.AP 2years
2026 2representative citing papers
The function −√(−u) is strictly convex for solutions u of det(u_{i⎵j})=1 on strictly convex domains in C².
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Brunn--Minkowski Inequality for the First Complex $\sigma_{2}$-Hessian Eigenvalue
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.
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Power Convexity of Solutions to the Complex Monge-Amp\`{e}re Equation $\det(u_{i\overline{j}})=1$ in Complex Dimension Two
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