Approximation of m-subharmonic functions on bounded domains in \mathbb Cⁿ

2017/11/15 by Dieu, Nguyen Quang, Dau Hoang Hung, Hung, Dau Hoang +4
Mathematics · #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1711.05657

Abstract

Let D be a bounded domain in \mathbb Cⁿ. We study approximation of (not necessarily bounded from above) m-subharmonic function D by continuous m-subharmonic ones defined on neighborhoods of D. We also consider the existence of a m-subharmonic function on D whose boundary values coincides with a given real valued continuous function on ∂ D except for a sufficiently small subset of ∂ D.

Related

• Subextension and approximation of m-subharmonic functions with given boundary values
• Approximation of m-subharmonic functions in weighted energy classes with given boundary values
• Hessian type equations for m-ω-subharmonic functions on bounded domains in \mathbb Cⁿ
• The Dirichlet problem for m-subharmonic functions on compact sets
• Maximal subextension and approximation of m-subharmonic function