%0 Journal Article
%T The weak Cartan property for the p-fine topology on metric spaces
%A Anders Bj£¿rn
%A Jana Bj£¿rn
%A Visa Latvala
%J Mathematics
%D 2013
%I arXiv
%X We study the p-fine topology on complete metric spaces equipped with a doubling measure supporting a p-Poincare inequality, 1 < p< oo. We establish a weak Cartan property, which yields characterizations of the p-thinness and the p-fine continuity, and allows us to show that the p-fine topology is the coarsest topology making all p-superharmonic functions continuous. Our p-harmonic and superharmonic functions are defined by means of scalar-valued upper gradients and do not rely on a vector-valued differentiable structure.
%U http://arxiv.org/abs/1310.8101v1