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}
}
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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