Trace Inequalities, isocapacitary inequalities and regularity of the complex Hessian equations

2022/01/06 by Jiaxiang Wang, Bin Zhou, Wang, Jiaxiang +1
Mathematics · #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2201.02061

openalex publication_date 2022/01/06 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the relations between trace inequalities(Sobolev and Moser-Trudinger type), isocapacitary inequalities and the regularity of the complex Hessian and Monge-Amp\`ere equations with respect to a general positive Borel measure. We obtain a quantitative characterization for these relations through properties of the capacity minimizing functions.

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