Calibration for minimal surfaces with free boundary and Cheeger-type problems
Analysis of PDEs
2025-11-06 v1 Optimization and Control
Abstract
We study a problem of minimal surfaces with free boundary written in the form of a non convex minimization problem. Our aim is to characterize optimal solutions by finding a suitable calibration field. A natural upper bound of the infimum is given by a variant of the Cheeger problem that we solve explicitly proving the optimality thanks to the construction of a cut-locus potential. The comparison with the original problem is then discussed in detail.
Cite
@article{arxiv.2511.03322,
title = {Calibration for minimal surfaces with free boundary and Cheeger-type problems},
author = {Guy Bouchitté and Minh Phan},
journal= {arXiv preprint arXiv:2511.03322},
year = {2025}
}
Comments
41 pages, 13 figures