31 mar 2017 -- 14:30
Aula Seminari, Dipartimento di Matematica, Pisa
Abstract.
In this talk I’ll describe the problem of filling submanifolds with topological or holomorphic disks. The case of geodesics on compact Riemannian surfaces with nonpositive scalar curvature will be treated. I will prove non existence of such disk filling, using several different tecniques. Two possible generalizations in higher dimension will be shown: – the product of geodesics on the product of compact Riemannian surfaces with nonpositive scalar curvature does not admit a holomorphic disk filling; – a minimal Lagrangian torus in a Kahler 4-manifold with nonpositive Ricci tensor does not admit an holomorphic filling with a solid torus.