Calculus of Variations and Geometric Measure Theory
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L. Ambrosio

Fine properties of sets of finite perimeter in doubling metric measure spaces

created on 30 Sep 2001
modified on 25 Sep 2014


Published Paper

Inserted: 30 sep 2001
Last Updated: 25 sep 2014

Journal: Set Valued Analysis
Volume: 10
Pages: 111-128
Year: 2002


In this paper we prove that the perimeter measure is concentrated on the essential boundary of the set and that it is representable by an Hausdorff-type measure. Moreover, the perimeter measure satisfies an asymptotic doubling condition useful for differentiation purposes. The results of this paper are valid in a general setting which includes any Carnot--Carathéodory space; we obtain them by a refinement of the techinques introduced in previou paper, relative to Ahlfors regular metric measure spaces.


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