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arXiv · 1405.0186

Characterizations of sets of finite perimeter using heat kernels in metric spaces

Niko Marola·Michele Miranda Jr.·Nageswari Shanmugalingam
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Abstract

The overarching goal of this paper is to link the notion of sets of finite perimeter (a concept associated with $N^{1,1}$-spaces) and the theory of heat semigroups (a concept related to $N^{1,2}$-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 ${\rm BV}$ functions in terms of a near-diagonal energy in this general setting.

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Niko Marola, Michele Miranda Jr., Nageswari Shanmugalingam. 2016-06-10. Characterizations of sets of finite perimeter using heat kernels in metric spaces. https://doi.org/10.1007/s11118-016-9560-3

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