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Boundary Regularity and Embedded Solutions for the Oriented Plateau Problem

1979
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Annals of Mathematics
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Any fixed C 2 Jordan curve F in R 3 is known to span an orientable minimal surface in several different senses. In the work of Douglas, Rado and Courant (see e.g. [3, IV, §4] ) the minimal surface occurs as an area-minimizing mapping from a fixed orientable surface of finite genus and may possibly have self-intersections. In the work of Fédérer and Fleming (see e.g. [4, §5]) the minimal surface, which occurs as the support of an area-minimizing rectifiable current, is necessarily embedded (away

doi:10.2307/1971233
fatcat:26bttxrx5zbnddpeai2zitj6ci