A classification of minimal cones in Rn x R+ and a counterexample to interior regularitiy of energy minimizing functions.

Ulrich Dierkes

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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.