Hölder regularity of three-dimensional minimal cones in $\mathbb {R}^{n}$
Volume 110 / 2014
Annales Polonici Mathematici 110 (2014), 227-246
MSC: Primary 49Q05; Secondary 49Q15.
DOI: 10.4064/ap110-3-2
Abstract
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.
