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arXiv · 1310.8101

The weak Cartan property for the p-fine topology on metric spaces

Anders Björn·Jana Björn·Visa Latvala
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Abstract

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.

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Anders Björn, Jana Björn, Visa Latvala. 2013-10-30. The weak Cartan property for the p-fine topology on metric spaces. https://doi.org/10.1512/iumj.2015.64.5527

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