Hölder regularity of three-dimensional minimal cones in $\mathbb {R}^{n}$

Tien Duc Luu¹

¹ Département de Mathématiques Bât. 425 Université Paris-Sud XI 91405 Orsay Cedex, France

Annales Polonici Mathematici, Tome 110 (2014) no. 3, pp. 227-246.

Résumé

We show the local Hölder regularity of Almgren minimal cones of dimension 3 in $\mathbb {R}^n$ away from their centers. The proof is almost elementary but we use the generalized theorem of Reifenberg. In the proof, we give a classification of points away from the center of a minimal cone of dimension 3 in $\mathbb {R}^n$, into types $\mathbb {P}$, $\mathbb {Y}$ and $\mathbb {T}$. We then treat each case separately and give a local Hölder parameterization of the cone.

Détail

DOI : 10.4064/ap110-3-2

Keywords: local lder regularity almgren minimal cones dimension mathbb away their centers proof almost elementary generalized theorem reifenberg proof classification points away center minimal cone dimension mathbb types mathbb mathbb mathbb treat each separately local lder parameterization cone