Perlen-Kolloquium: Camillo De Lellis

The Plateau problem, named by Henry Lebesgue after the Belgian physicist, consists in finding the surface of least area which spans a given contour. In order to tackle such question, generations of mathematicians have investigated the very fundamental notions of "surface", "boundary" and "area", proposing a variety of dierent theories. In this talk I will give a brief exposition of the so-called theory of currents, introduced by Federer and Fleming in the 60es after the pioneering work of De Giorgi in the case of hypersurfaces. I will then discuss an open question relating the shapes of the contour and that of the minimizer, posed by Almgren in the early eighties and recently solved in a joint work with Guido de Philippis, Jonas Hirsch and Annalisa Massaccesi.

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