10 nov 2016 -- 17:30
Sala Riunioni, Dipartimento di Matematica, Pisa
The existence of solutions for the Plateau problem is not yet completely settled, and this is strictly related to the fact that the Plateau problem itself is not clearly defined. I will first present an improvement of the approach to Plateau's type problems proposed by Amato, Bellettini and Paolini, which is based on the minimization of the total variation of constrained BV functions on suitebaly chosen covering spaces. Then, I will define calibrations for the Steiner problem, and explain the differences between our approach and the previous ones (Brakke, Lawlor-Morgan, Marchese-Massaccesi). I will conclude by giving some examples. This is a joint project with Giovanni Bellettini, Marcello Carioni and Maurizio Paolini.