Calculus of Variations and Geometric Measure Theory

J. Kinnunen - R. Korte - A. Lorent - N. Shanmugalingam

Regularity of sets with quasiminimal boundary surfaces in metric spaces

created by lorent on 16 May 2011
modified on 18 Feb 2014


Published Paper

Inserted: 16 may 2011
Last Updated: 18 feb 2014

Journal: J. Geom. Anal.
Volume: 23
Number: 4
Pages: 1607-1640
Year: 2013


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