INVERSE CURVATURE FLOWS AND GEOMETRIC INEQUALITIES |
Julian Scheuer |
Thursday, 2018-01-18 16:00 |
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In recent years curvature flows have played a crucial role in proving important geometric theorems. For instance, the Ricci flow lead to a proof of the Poincare conjecture, and the inverse mean curvature flow (IMCF) was crucial in the proof of the Riemannian Penrose inequality. In this talk we present further applications of the IMCF. First we review, how classical geometric inequalities, such as the Minkowski inequality for closed convex hypersurfaces, can be generalised to a wider class of hypersurfaces using curvature flows. Secondly, we present new estimates for a Willmore-type energy of hypersurfaces with boundary, satisfying a perpendicular Neumann-type condition on the unit sphere. The crucial ingredient is the IMCF with boundary conditions. |