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