18 jan 2017 -- 16:00 [open in google calendar]

Scuola Normale Superiore, Aula Curie

**Abstract.**

Let (M,g) be a Riemannian manifold with nonempty boundary, and suppose that its curvature is (lower or upper) bounded. In this talk we will approach the Riemannian extension problem for (M,g): can (M,g) be realized as a domain in a "larger" manifold (N,h), complete and without boundary, in such a way that the same curvature bound is preserved? We will present three classes of results: (1) a general existence theorem for a complete extension in the absence of curvature constraints; (2) some topological obstructions to the existence of an extension when a bound on its Ricci or sectional curvature is imposed; (3) some existence results, notably under a convexity condition on the boundary. This is a joint project with Stefano Pigola.