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arXiv · 2510.02299

Uniqueness in the Plateau problem for calibrated currents

Bryan Dimler·Chen-Kuan Lee
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Abstract

We show that every compactly supported smoothly calibrated integral current with connected $C^{3,\alpha}$ boundary is the unique solution to the oriented Plateau problem for its boundary data. The same holds true for compactly supported $``$continuously calibrated$"$ integral flat chains. This is proved as a consequence of the boundary regularity theory for area-minimizing currents and a unique continuation argument in the spirit of Frank Morgan. In codimension one, the argument yields a sufficient condition for uniqueness in the oriented Plateau problem expressed in terms of the regularity of the calibrating form.

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Bryan Dimler, Chen-Kuan Lee. 2025-10-02. Uniqueness in the Plateau problem for calibrated currents. https://arxiv.org/abs/2510.02299

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