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Regularity of Sets with Quasiminimal Boundary Surfaces in Metric Spaces |
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| Authors: | Juha Kinnunen Riikka Korte Andrew Lorent Nageswari Shanmugalingam |
| Institution: | 1. Department of Mathematics, Aalto University, P.O. Box 11100, 00076, Aalto, Finland 2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, Gustaf H?llstr?min katu 2b, 00014, Helsinki, Finland 3. Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH, 45221–0025, USA |
| Abstract: | 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. |
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