A Runge theorem for subharmonic functions on Riemannian manifolds

Abstract

Approximation theory is a rich and deeply developed field. This article presents an approximation theorem of Runge type for subharmonic functions on compact subsets of non-compact Riemannian manifolds.

UNIFORM APPROXIMATION ON RIEMANNIAN MANIFOLDS BY SOLUTIONS OF THE EQUATION ∆u = f

“…is harmonic on N. By [2, Theorem 9.3], there exists a harmonic function h on Ω such that . sup should be compared with our definition of subharmonic singular function presented in [4] and [5].…”

A Runge Theorem for Subharmonic Functions on Closed Subsets of Riemannian Manifolds

“…In a recent article, the author proved an approximation theorem for subharmonic functions on compact subsets of non-compact Riemannian manifolds ( [1]). The purpose of this work is to extend this result to subharmonic functions on closed subsets of non-compact Riemannian manifolds.…”