When a minimal submanifold with boundary on a given Riemannian manifold meets another hypersurface orthogonally, it is said to be a free boundary minimal submanifold. This constraint is very natural from a variational point of view. We will talk about some recent progress on the understanding of compact free boundary minimal hypersurfaces in various ambient domains. In particular, we will discuss our work on classification of free boundary minimal surfaces in the unit ball of the Euclidean space (joint with I Nunes, UFMA), on some general index estimates, and on convergence of sequences of free boundary minimal hypersurfaces under various assumptions (joint with A. Carlotto, ETH, and B. Sharp, Warwick).
Free boundary minimal hypersurfaces
Tue, 14/11/2017 - 15:00