Regularity of sets with quasiminimal boundary surfaces in metric spaces
Analysis of PDEs
2011-05-17 v1
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
Cite
@article{arxiv.1105.3058,
title = {Regularity of sets with quasiminimal boundary surfaces in metric spaces},
author = {Juha Kinnunen and Riikka Korte and Andrew Lorent and Nageswari Shanmugalingam},
journal= {arXiv preprint arXiv:1105.3058},
year = {2011}
}
Comments
31 pages