Published Paper
Inserted: 16 may 2011
Last Updated: 18 feb 2014
Journal: J. Geom. Anal.
Volume: 23
Number: 4
Pages: 1607-1640
Year: 2013
Abstract:
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.
Keywords: functions of bounded variation, minimal surfaces, perimeter
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