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

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Marola , N , Miranda , M & Shanmugalingam , N 2016 , ' Characterizations of Sets of Finite Perimeter Using Heat Kernels in Metric Spaces ' , Potential Analysis , vol. 45 , no. 4 , pp. 609-633 . https://doi.org/10.1007/s11118-016-9560-3

Title: Characterizations of Sets of Finite Perimeter Using Heat Kernels in Metric Spaces
Author: Marola, Niko; Miranda, Michele; Shanmugalingam, Nageswari
Other contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2016-11
Language: eng
Number of pages: 25
Belongs to series: Potential Analysis
ISSN: 0926-2601
DOI: https://doi.org/10.1007/s11118-016-9560-3
URI: http://hdl.handle.net/10138/224137
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-Poincar, 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 near-diagonal energy in this general setting.
Subject: Bakry-Emery condition
Bounded variation
Dirichlet form
Doubling measure
Heat kernel
Heat semigroup
Isoperimetric inequality
Metric space
Perimeter
Poincare inequality
Sets of finite perimeter
Total variation
LOCAL DIRICHLET SPACES
CURVATURE-DIMENSION CONDITION
BOUNDED VARIATION
ISOPERIMETRIC INEQUALITY
RIEMANNIAN-MANIFOLDS
SOBOLEV SPACES
SEMIGROUP
DEFINITIONS
RECURRENCE
111 Mathematics
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