The Dirichlet problem for the complex Hessian operator in the class N_m(H)

2017/12/19 by Ayoub El-Gasmi, El-Gasmi, Ayoub
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1712.06911

openalex publication_date 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that, in a m-hyperconvex domain in ℂⁿ, if a non-negative Borel measure is dominated by a complex Hessian measure, then it is a complex Hessian measure of a function in the class N_m(H). This is an extension of P. Åhg, U. Cegrell, R. Czyż and P.H. Hiep's result in \citeACCH.

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