Seminar Analysis: Camillo De Lellis (University of Zurich)

Regularity theory for area-minimizing currents

A well-known theorem of Almgren shows that area-minimizing integral k-dimensional currents in a Riemannian manifold of arbitrary dimension N are regular up to a set of closed dimension of Hausdorff dimension at most N-2. In a joint work with Emanuele Spadaro we give a much shorter proof of this statement in the euclidean setting, following the general program of Almgren but introducing new ideas at the various steps. In this talk I will explain some if these ideas. A generalization of our proof to the Riemannian case is work in progress.

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