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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}
}

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31 pages