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

Michael Goldman (1) , Matteo Novaga (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 Dipartimento di Matematica Pura e Applicata [Padova]

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: prescribed mean curvature surfaces; minimal surfaces; homogenization

Domains: Analysis of PDEs [math.AP]; Differential Geometry [math.DG]; Optimization and Control [math.OC]

Michael Goldman, Matteo Novaga. Volume-constrained minimizers for the prescribed curvature problem in periodic media. 2012. ⟨hal-00580074v3⟩