Regularity of sets with quasiminimal boundary surfaces in metric spaces

Details Regularity of sets with quasiminimal boundary surfaces in metric spaces Regularity of sets with quasiminimal boundary surfaces in metric spaces

2011-05-16

arxiv.org/abs/1105.3058v1

Mathematics

Analysis of PDEs

31 pages

Scientific paper

This paper studies regularity of perimiter quasiminimizing sets in metric measure spaces with a doubling measure and a Poincare inequality. The main result shows that the measure theoretic boundary of a quasiminimizing set coincides with the topological boundary. We also show that such a set has finite Minkowski content and apply the regularity theory to study rectifiability issues related to quasiminimal sets in strong A_{\infty}-weighted Euclidean case.

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