Analysis reveals optimal calibration for free boundary minimal surfaces, suggesting connections to Cheeger problems.
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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Bouchitté et al. (2025) studied this question.
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