Camillo De Lellis (UZH) Pieces of soap films: boundaries and Plateau's problem скачать в хорошем качестве

Camillo De Lellis (UZH) Pieces of soap films: boundaries and Plateau's problem

The Plateau problem, named by Henry Lebesgue after the Belgian physicist, consists in finding the surface of least area which spans a given contour: Plateau discovered that soap films obey that simple energy principle. In order to investigate the question, generations of mathematicians have investigated the very fundamental notions of “surface”, “boundary” and “area”, proposing a variety of different 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.