Riikka Korte, Panu Lahti, Nageswari Shanmugalingam
Published 2014-10-08Version 1
In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.
Classification of metric measure spaces and their ends using $p$-harmonic functions
Alberti's rank one theorem and quasiconformal mappings in metric measure spaces
The space of spaces: curvature bounds and gradient flows on the space of metric measure spaces
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