naa a22 4500 51081090X CHVBK 20180411083442.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s12220-012-9299-z doi (NATIONALLICENCE)springer-10.1007/s12220-012-9299-z Regularity of Sets with Quasiminimal Boundary Surfaces in Metric Spaces [Elektronische Daten] [Juha Kinnunen, Riikka Korte, Andrew Lorent, Nageswari Shanmugalingam] 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. Mathematica Josephina, Inc., 2012 Functions of bounded variation nationallicence Perimeter nationallicence Minimal surfaces nationallicence Kinnunen Juha Department of Mathematics, Aalto University, P.O. Box 11100, 00076, Aalto, Finland aut Korte Riikka Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2b, P.O. Box 68, 00014, Helsinki, Finland aut Lorent Andrew Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, 45221-0025, Cincinnati, OH, USA aut Shanmugalingam Nageswari Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, 45221-0025, Cincinnati, OH, USA aut Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1607-1640 1050-6926 23:4<1607 2013 23 12220 https://doi.org/10.1007/s12220-012-9299-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-012-9299-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kinnunen Juha Department of Mathematics, Aalto University, P.O. Box 11100, 00076, Aalto, Finland aut NATIONALLICENCE 700 1- Korte Riikka Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2b, P.O. Box 68, 00014, Helsinki, Finland aut NATIONALLICENCE 700 1- Lorent Andrew Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, 45221-0025, Cincinnati, OH, USA aut NATIONALLICENCE 700 1- Shanmugalingam Nageswari Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, 45221-0025, Cincinnati, OH, USA aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/4(2013-10-01), 1607-1640 1050-6926 23:4<1607 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer