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Peer-reviewedCC BY-NC-ND 4.0Journal of Convex Analysis

Calibrations for Minimal Surfaces with Free Boundary and Cheeger-Type Problems

  • Guy Bouchitté
  • Minh Phan
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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.

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Cite

BibTeXRIS
BibTeX
@article{bouchitte2026calibrations,
  title = {{Calibrations for Minimal Surfaces with Free Boundary and Cheeger-Type Problems}},
  author = {Guy Bouchitté and Minh Phan},
  journal = {Journal of Convex Analysis},
  year = {2026},
  month = oct,
  doi = {10.68381/jca33041},
  url = {https://univ-tln.hal.science/hal-05846468v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - JOUR
TI  - Calibrations for Minimal Surfaces with Free Boundary and Cheeger-Type Problems
AU  - Guy Bouchitté
AU  - Minh Phan
PY  - 2026
DA  - 2026/10/31
JO  - Journal of Convex Analysis
DO  - 10.68381/jca33041
UR  - https://univ-tln.hal.science/hal-05846468v1
AB  - 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.
SN  - 0944-6532
SN  - 2363-6394
ER  -