Volume-constrained minimizers for the prescribed curvature problem in periodic media
Analysis of PDEs
2013-03-18 v5 Differential Geometry
Optimization and Control
Abstract
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.
Keywords
Cite
@article{arxiv.1103.5161,
title = {Volume-constrained minimizers for the prescribed curvature problem in periodic media},
author = {Michael Goldman and Matteo Novaga},
journal= {arXiv preprint arXiv:1103.5161},
year = {2013}
}
Comments
In this version the statement of Lemma 2.5 has been corrected with respect to the published version