Size minimizing surfaces
[Surfaces minimisantes]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 1, pp. 37-101.

Nous obtenons un nouveau théorème d’existence relatif au problème de Plateau dans l’espace euclidien de dimension 3. Ce faisant, nous comparons les approches d’E.R. Reifenberg d’une part, et de H. Federer et W.H. Fleming d’autre part. Un pas technique important consiste à démontrer qu’on peut approcher tout ensemble compact et rectifiable, en mesure de Hausdorff et en distance de Hausdorff, par une surface localement acyclique ayant le même bord.

We prove a new existence theorem pertaining to the Plateau problem in 3-dimensional Euclidean space. We compare the approach of E.R. Reifenberg with that of H. Federer and W.H. Fleming. A relevant technical step consists in showing that compact rectifiable surfaces are approximatable in Hausdorff measure and in Hausdorff distance by locally acyclic surfaces having the same boundary.

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     title = {Size minimizing surfaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
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     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 42},
     number = {1},
     year = {2009},
     doi = {10.24033/asens.2090},
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     url = {https://www.numdam.org/articles/10.24033/asens.2090/}
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Pauw, Thierry De. Size minimizing surfaces. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 1, pp. 37-101. doi : 10.24033/asens.2090. https://www.numdam.org/articles/10.24033/asens.2090/

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