Sala Seminari (Dip. Matematica).
In this talk, we consider the existence problem for weak solutions of the Inverse Mean Curvature Flow on a complete manifold with only a Ricci lower bound. Solutions either issue from a point or from the boundary of a relatively compact open set. To prove their existence in the sense of Huisken-Ilmanen, we follow the strategy pioneered by J. Moser that uses approximation by p-Laplacian kernels. In particular, we prove new and sharp gradient estimates for the kernel of the p-Laplacian on M via the study of the fake distance associated to it. We address the compactness of the flowing hypersurfaces, and time permitting some monotonicity formulas in the spirit of Geroch’s one. This is joint work with M. Rigoli and A.G. Setti.