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  "body": "\n## Summary\n\nAn area-minimizing current is an [[integral current|EG4AJVEFT2]] whose mass is not larger than that of any other integral current with the same boundary.\nIt is the solution concept of the Plateau problem in geometric measure theory, and it generalises oriented [[minimal surfaces|41X0YW2R9N]] that minimise area.\nSuch currents exist for every boundary that bounds some integral current.\nTheir regularity is a central topic: they are smooth away from a singular set of small dimension.\n\n## Explanations\n\n### L1 human\n\nTake a closed wire loop and ask for the surface of least area spanning it, counting area with orientation and multiplicity.\nAn area-minimizing current is such a least-area surface in a generalised sense, so that one exists even when no smooth one does.\nFor a round circle in space, the flat disc is area-minimizing; a hemisphere with the same rim is not, because it has twice the area.\nIn high dimensions minimisers can have singular points, for example cones over products of spheres.\n",
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