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On some properties of three-dimensional minimal sets in 4
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 3, pp. 465-493.

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

On prouve dans cet article la régularité Höldérienne pour les ensembles minimaux au sens d’Almgren de dimension 3 dans 4 autour d’un point de type 𝕐 et dans le cas d’un ensemble Mumford-Shah minimal dans 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 4 autour d’un point singulier et une propriété des ensembles Mumford-Shah minimaux dans 4 .

Published online:
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, Toulouse},
     volume = {Ser. 6, 22},
     number = {3},
     year = {2013},
     doi = {10.5802/afst.1379},
     zbl = {1290.49093},
     mrnumber = {3113023},
     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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