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@article{faucris.115903524,
abstract = {We consider - in the setting of geometric measure theory - hypersurfaces T (of codimension one) with prescribed boundary B in Euclidean n+1 space which maximize volume (i.e. T together with a fixed hypersurface T0 encloses oriented volume) subject to a mass constraint. We prove existence and optimal regularity of solutions T of such variational problems and we show that, on the regular part of its support, T is a classical hypersurface of constant mean curvature. Wc also prove that the solutions T become more and more spherical as the value m of the mass constraint approaches},
author = {Duzaar, Frank},
doi = {10.1007/BF02567956},
faupublication = {no},
journal = {Manuscripta Mathematica},
note = {UnivIS-Import:2015-03-05:Pub.1996.nat.dma.lma2.hypers},
pages = {303-315},
peerreviewed = {Yes},
title = {{Hypersurfaces} with constant mean curvature and prescribed area},
url = {http://www.springerlink.com/content/03k827467654842w/fulltext.pdf},
volume = {91},
year = {1996}
}