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

Tom 110 / 2014

Tien Duc Luu Annales Polonici Mathematici 110 (2014), 227-246 MSC: Primary 49Q05; Secondary 49Q15. DOI: 10.4064/ap110-3-2

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.

Autorzy

  • Tien Duc LuuDépartement de Mathématiques
    Bât. 425
    Université Paris-Sud XI
    91405 Orsay Cedex, France
    e-mail

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