Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

Streszczenie

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.