$p$-harmonic functions on complete manifolds with a weighted Poincaré inequality

Abstract

In this paper, we consider $p$-harmonic functions on complete Riemannian manifolds and give different proofs of some main theorems by Chang-Chen-Wei, in [3]. Moreover, we are able to refine their results in case of weakly $p$-harmonic functions. Some applications to study the connectedness at infinity of stable minimal hypersurfaces are also given.