Uniqueness in the Plateau problem for calibrated currents

2025/10/02 by Dimler, Bryan, Lee, Chen-Kuan · 1 citation
#49Q15 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.02299

Abstract

We show that every compactly supported smoothly calibrated integral current with connected C^3,α 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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Cited by

• Special Lagrangians with multiple isolated singularities

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