Volume no :31, Issue no: 1, January

Journal of Mathematical Sciences: Advances and Applications

A RUNGE THEOREM FOR SUBHARMONIC FUNCTIONS ON CLOSED SUBSETS OF RIEMANNIAN MANIFOLDS

Author's: Pierre Blanchet
Pages: [37] - [41]
Received Date: January 29, 2015
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121451

Abstract

Let F be a closed subset of a non-compact Riemannian manifold This article presents a proof that every continuous and subharmonic function on a neighbourhood of F can be uniformly approximated on F by a function, which is and subharmonic on except for singularities.

Keywords

subharmonic functions, subharmonic approximation, Newtonian functions, Runge theorem, Riemannian manifolds.