Regularity of Sets with Quasiminimal Boundary Surfaces in Metric Spaces

By Juha Kinnunen, R. Korte, A. Lorent, Nageswari Shanmugalingam. Journal of Geometric Analysis, 2011

67 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a240923e80d76c903ad4bfe9ce328235f5f85d78

Citations in the corpus

• The quantitative isoperimetric inequality and related topics (2015, unknown): “This is indeed the content of the next result which was first proved by David and Semmes in [51] and then extended by Kinnunen, Korte, Lorent and Shanmugalingam [88] to the metric spaces setting.”