arXiv:1103.5161 Abstract | arXiv Analytics

arXiv:1103.5161 [math.AP]Abstract References Reviews Resources

Volume-constrained minimizers for the prescribed curvature problem in periodic media

Published 2011-03-26, updated 2013-03-15Version 5

We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also show convergence after rescaling of the volume-constrained minimizers towards a suitable Wulff Shape, when the volume tends to infinity.

Comments: In this version the statement of Lemma 2.5 has been corrected with respect to the published version

Categories: math.AP, math.DG, math.OC

Keywords: prescribed curvature problem, periodic media, volume-constrained minimizers, construct compact approximate solutions, prescribed mean curvature problem

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