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Mathematical Colloquium: Boundary regularity of area-minimizing surfaces and a question of Almgren

Camillo De Lellis
Institut fuer Mathematik, Universitat Zurich
Thursday, May 17, 2018 - 16:00

The theory of integral currents, developed by Federer and Fleming in the 60s, gives a powerful framework to solve the Plateau's problem in an arbitrary Riemannian manifold and for every dimension and codimension. The interior and boundary regularity theories for the codimension one case are rather well understood since the end of the seventies. In higher codimension a far-reaching interior regularity theory was developed by Almgren in his celebrated Big Regularity Paper (originally a typewritten manuscript of more than 1700 pages), whereas the current literature fails to provide even
a single regular point at the boundary unless we require rather restrictive assumptions on the ambient space. In a joint work with Guido de Philippis, Annalisa Massaccesi and Jonas Hirsch we provide a first general boundary regularity result, which also allows to answer to a question of Almgren on the connectivity of the minimizer.

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