Research demonstrates unique solutions to the oriented plateau problem in calibrated currents, suggesting strong connections to boundary regularity.
We show that every compactly supported calibrated integral current with connected C3,α boundary is the unique solution to the oriented Plateau problem for its boundary data. This is proved as a consequence of the boundary regularity theory for area-minimizing currents and classical unique continuation principles adapted to the minimal surface system.
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Dimler et al. (2025) studied this question.
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