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

2011/03/26 by Michael Goldman, Goldman, Michael, Matteo Novaga +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Optimization and Control (math.OC) #math.AP #math.DG #math.OC

paper · pdf · doi:10.48550/arxiv.1103.5161

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

arxiv created 2013/03/15 · arxiv updated 2013/03/18

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.

Related

• Volume constrained minimizers of the fractional perimeter with a potential energy
• On the shape of compact hypersurfaces with almost constant mean curvature
• Spectral Prescribed Mean Curvature
• A double mean field equation related to a curvature prescription problem
• The Dirichlet problem for a prescribed mean curvature equation