We show the local Hölder regularity of Almgren minimal cones of dimension 3 in ℝⁿ 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 ℝⁿ, into types ℙ, 𝕐 and 𝕋. We then treat each case separately and give a local Hölder parameterization of the cone.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-3-2,
author = {Tien Duc Luu},
title = {Holder regularity of three-dimensional minimal cones in Rn},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {227-246},
zbl = {1293.49104},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-3-2}
}
Tien Duc Luu. Hölder regularity of three-dimensional minimal cones in ℝⁿ. Annales Polonici Mathematici, Tome 111 (2014) pp. 227-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-3-2/