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The classical Plateau problem and the topology of three-dimensional manifolds: the embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's Lemma

William H Meeks III Shing-Tung Yau

Geometric Analysis and Geometric Topology mathscidoc:1912.43486

Topology, 21, (4), 409-442, 1982.1
NRODUCTION LET y be a rectifiable Jordan curve in three-dimensional euclidean space. Answering an old question, whether y can bound a surface with minimal area, Douglas [l I] and Rad6 [45](independently) found a minimal surface spanning y which is parametrized by the disk. This minimal surface has minimal area among all Lipschitz maps from the disk into R3 which span y. The question whether this solution has branch points or not was finally settled by Osserman [42], who proved that there are no interior true branch points, and by Gulliver [lS], who proved that there are no interior false branch points.
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@inproceedings{william1982the,
  title={The classical Plateau problem and the topology of three-dimensional manifolds: the embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's Lemma},
  author={William H Meeks III, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203543233305050},
  booktitle={Topology},
  volume={21},
  number={4},
  pages={409-442},
  year={1982},
}
William H Meeks III, and Shing-Tung Yau. The classical Plateau problem and the topology of three-dimensional manifolds: the embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's Lemma. 1982. Vol. 21. In Topology. pp.409-442. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203543233305050.
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