On some properties of three-dimensional minimal sets in ${\mathbb{R}}^4$

Tien Duc Luu

doi:10.5802/afst.1379

On some properties of three-dimensional minimal sets in

ℝ^{4}

Tien Duc Luu

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 3, pp. 465-493.

Abstract
Abstract

We prove in this paper the Hölder regularity of Almgren minimal sets of dimension 3 in $ℝ^{4}$ around a $𝕐$ -point and the existence of a point of particular type of a Mumford-Shah minimal set in $ℝ^{4}$ , which is very close to a $𝕋$ . This will give a local description of minimal sets of dimension 3 in $ℝ^{4}$ around a singular point and a property of Mumford-Shah minimal sets in $ℝ^{4}$ .

On prouve dans cet article la régularité Höldérienne pour les ensembles minimaux au sens d’Almgren de dimension 3 dans $ℝ^{4}$ autour d’un point de type $𝕐$ et dans le cas d’un ensemble Mumford-Shah minimal dans $ℝ^{4}$ qui est très proche d’un $𝕋$ , l’existence d’un point avec une densité particulière. Cela donne une description locale des ensembles minimaux de dimension 3 dans $ℝ^{4}$ autour d’un point singulier et une propriété des ensembles Mumford-Shah minimaux dans $ℝ^{4}$ .

MR Zbl

DOI: 10.5802/afst.1379

@article{AFST_2013_6_22_3_465_0,
     author = {Tien Duc Luu},
     title = {On some properties of three-dimensional minimal sets in ${\mathbb{R}}^4$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {465--493},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 22},
     number = {3},
     year = {2013},
     doi = {10.5802/afst.1379},
     mrnumber = {3113023},
     zbl = {1290.49093},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1379/}
}

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Tien Duc Luu. On some properties of three-dimensional minimal sets in ${\mathbb{R}}^4$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 3, pp. 465-493. doi : 10.5802/afst.1379. https://afst.centre-mersenne.org/articles/10.5802/afst.1379/

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