# Characterizations of Sets of Finite Perimeter Using Heat Kernels in Metric Spaces

@article{Marola2016CharacterizationsOS,
title={Characterizations of Sets of Finite Perimeter Using Heat Kernels in Metric Spaces},
author={Niko Marola and Michele Miranda and Nageswari Shanmugalingam},
journal={Potential Analysis},
year={2016},
volume={45},
pages={609-633}
}
• Published 1 May 2014
• Mathematics
• Potential Analysis
The overarching goal of this paper is to link the notion of sets of finite perimeter (a concept associated with N1,1-spaces) and the theory of heat semigroups (a concept related to N1,2-spaces) in the setting of metric measure spaces whose measure is doubling and supports a 1-Poincaré inequality. We prove a characterization of sets of finite perimeter in terms of a short time behavior of the heat semigroup in such metric spaces. We also give a new characterization of BV functions in terms of a…
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