Hölder regularity of three-dimensional minimal cones in ℝⁿ

Tien Duc Luu

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The following text is a minor modification of the transparencies that were used in the conference; please excuse the often telegraphic style. The main goal of the series of lectures is a presentation (with some proofs) of Jean Taylor’s celebrated theorem on the regularity of almost minimal sets of dimension $2$ in $ℝ^{3}$ , and a few more recent extensions or perspectives. Some of the results presented below are work of, or with T. De Pauw, V. Feuvrier A. Lemenant, and T. Toro. ...