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arXiv · 1105.3058

Regularity of sets with quasiminimal boundary surfaces in metric spaces

Juha Kinnunen·Riikka Korte·Andrew Lorent·Nageswari Shanmugalingam
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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.

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Juha Kinnunen, Riikka Korte, Andrew Lorent, Nageswari Shanmugalingam. 2011-05-16. Regularity of sets with quasiminimal boundary surfaces in metric spaces. https://doi.org/10.1007/s12220-012-9299-z

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