Kolloquien und Oberseminare Übersicht Detail

Speaker:
Prof. Dr. Thomas Schmidt (Universität Hamburg)

A classical approach to Plateau’s problem for hypersurfaces in R^n is based on minimization of the (generalized measure-theoretic) perimeter and in this form goes back to works of Caccioppoli, De Giorgi, and Miranda. More generally, Massari has shown in the 70s that minimization of the perimeter plus a volume term can produce hypersurfaces of prescribed L^p mean curvature in R^n. The talk aims at an extension of these classical results by considering the perimeter plus a general measure term. The focus will be on the study of this new functional and more precisely on recent results on lower semicontinuity, existence of minimizers, and symmetric model configurations.