Regularity of Sets with Quasiminimal Boundary Surfaces in Metric Spaces

摘要

This paper studies regularity of perimeter quasiminimizing sets in metric measure spaces with a doubling measure and a Poincaré 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 the strong A_∞-weighted Euclidean case.