| Abstract: |
| In this talk, we consider the existence problem for weak solutions of the Inverse Mean Curvature Flow on a complete manifold with 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, as well as monotonicity formulas in the spirit of Geroch`s one. |
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