Hölder regularity of two-dimensional almost-minimal sets in n

Guy David[1]

  • [1] Mathématiques, Bâtiment 425, Université de Paris-Sud 11, 91 405 Orsay Cedex, France

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

  • Volume: 18, Issue: 1, page 65-246
  • ISSN: 0240-2963

Abstract

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We give a different and probably more elementary proof of a good part of Jean Taylor’s regularity theorem for Almgren almost-minimal sets of dimension 2 in 3 . We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor’s result to almost-minimal sets of dimension 2 in n , and give the expected characterization of the closed sets E of dimension 2 in 3 that are minimal, in the sense that H 2 ( E F ) H 2 ( F E ) for every closed set F such that there is a bounded set B so that F = E out of B and F separates points of 3 B that E separates.

How to cite

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David, Guy. "Hölder regularity of two-dimensional almost-minimal sets in $\mathbb{R}^n$." Annales de la faculté des sciences de Toulouse Mathématiques 18.1 (2009): 65-246. <http://eudml.org/doc/10108>.

@article{David2009,
abstract = {We give a different and probably more elementary proof of a good part of Jean Taylor’s regularity theorem for Almgren almost-minimal sets of dimension $2$ in $\{\mathbb\{R\}\}^3$. We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor’s result to almost-minimal sets of dimension $2$ in $\mathbb\{R\}^n$, and give the expected characterization of the closed sets $E$ of dimension $2$ in $\{\mathbb\{R\}\}^3$ that are minimal, in the sense that $H^2(E\setminus F) \le H^2(F\setminus E)$ for every closed set $F$ such that there is a bounded set $B$ so that $F=E$ out of $B$ and $F$ separates points of $\{\mathbb\{R\}\}^3 \setminus B$ that $E$ separates.},
affiliation = {Mathématiques, Bâtiment 425, Université de Paris-Sud 11, 91 405 Orsay Cedex, France},
author = {David, Guy},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {regularity theorem; almost-minimal sets of dimension 2 in },
language = {eng},
month = {6},
number = {1},
pages = {65-246},
publisher = {Université Paul Sabatier, Toulouse},
title = {Hölder regularity of two-dimensional almost-minimal sets in $\mathbb\{R\}^n$},
url = {http://eudml.org/doc/10108},
volume = {18},
year = {2009},
}

TY - JOUR
AU - David, Guy
TI - Hölder regularity of two-dimensional almost-minimal sets in $\mathbb{R}^n$
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2009/6//
PB - Université Paul Sabatier, Toulouse
VL - 18
IS - 1
SP - 65
EP - 246
AB - We give a different and probably more elementary proof of a good part of Jean Taylor’s regularity theorem for Almgren almost-minimal sets of dimension $2$ in ${\mathbb{R}}^3$. We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor’s result to almost-minimal sets of dimension $2$ in $\mathbb{R}^n$, and give the expected characterization of the closed sets $E$ of dimension $2$ in ${\mathbb{R}}^3$ that are minimal, in the sense that $H^2(E\setminus F) \le H^2(F\setminus E)$ for every closed set $F$ such that there is a bounded set $B$ so that $F=E$ out of $B$ and $F$ separates points of ${\mathbb{R}}^3 \setminus B$ that $E$ separates.
LA - eng
KW - regularity theorem; almost-minimal sets of dimension 2 in
UR - http://eudml.org/doc/10108
ER -

References

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