caa a22 4500 445843454 CHVBK 20180317145351.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00526-010-0346-y doi (NATIONALLICENCE)springer-10.1007/s00526-010-0346-y Wenger Stefan Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan Street, 60607-7045, Chicago, IL, USA aut Compactness for manifolds and integral currents with bounded diameter and volume [Elektronische Daten] [Stefan Wenger] By Gromov's compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance. Working in the class of oriented k-dimensional Riemannian manifolds (with boundary) and, more generally, integral currents in metric spaces in the sense of Ambrosio-Kirchheim and replacing the Hausdorff distance with the filling volume or flat distance, we prove an analogous compactness theorem in which however we only assume uniform bounds on volume and diameter. Springer-Verlag, 2010 Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 423-448 0944-2669 40:3-4<423 2011 40 526 https://doi.org/10.1007/s00526-010-0346-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00526-010-0346-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wenger Stefan Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan Street, 60607-7045, Chicago, IL, USA aut NATIONALLICENCE 773 0- Calculus of Variations and Partial Differential Equations Springer-Verlag 40/3-4(2011-03-01), 423-448 0944-2669 40:3-4<423 2011 40 526 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer