Mixed Hessian inequalities and uniqueness in the class E(X,ω,m)

2014/04/24 by Sławomir Dinew, Chinh H. Lu, Dinew, Sławomir +1
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1404.6202

arxiv created 2014/04/24 · openalex publication_date 2014/04/24 · arxiv updated 2014/04/25 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We prove a general inequality for mixed Hessian measures by global arguments. Our method also yields a simplification for the case of complex Monge-Ampère equation. Exploiting this and using Kołodziej's mass concentration technique we also prove the uniqueness of the solutions to the complex Hessian equation on compact Kähler manifolds in the case of probability measures vanishing on m-polar sets.

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