Size minimizing surfaces

Thierry De Pauw

Annales scientifiques de l'École Normale Supérieure (2009)

  • Volume: 42, Issue: 1, page 37-101
  • ISSN: 0012-9593

Abstract

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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.

How to cite

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Pauw, Thierry De. "Size minimizing surfaces." Annales scientifiques de l'École Normale Supérieure 42.1 (2009): 37-101. <http://eudml.org/doc/272198>.

@article{Pauw2009,
abstract = {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.},
author = {Pauw, Thierry De},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Plateau problem; rectiviable current; smooth compact 1-dimensional submanifold ; algebraic boundary},
language = {eng},
number = {1},
pages = {37-101},
publisher = {Société mathématique de France},
title = {Size minimizing surfaces},
url = {http://eudml.org/doc/272198},
volume = {42},
year = {2009},
}

TY - JOUR
AU - Pauw, Thierry De
TI - Size minimizing surfaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2009
PB - Société mathématique de France
VL - 42
IS - 1
SP - 37
EP - 101
AB - 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.
LA - eng
KW - Plateau problem; rectiviable current; smooth compact 1-dimensional submanifold ; algebraic boundary
UR - http://eudml.org/doc/272198
ER -

References

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