Hypersurfaces with constant mean curvature and prescribed area

Duzaar F (1996)

Publication Type: Journal article

Publication year: 1996


Publisher: Springer Verlag (Germany)

Book Volume: 91

Pages Range: 303-315

Journal Issue: 3

URI: http://www.springerlink.com/content/03k827467654842w/fulltext.pdf

DOI: 10.1007/BF02567956


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 ∞.

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Duzaar, F. (1996). Hypersurfaces with constant mean curvature and prescribed area. Manuscripta Mathematica, 91(3), 303-315. https://dx.doi.org/10.1007/BF02567956


Duzaar, Frank. "Hypersurfaces with constant mean curvature and prescribed area." Manuscripta Mathematica 91.3 (1996): 303-315.

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