Tristan Riviere and Ben Sharp
16:15 Uhr | Tristan Riviere (ETH) | Some results on the calculus of variations of Riemann surfaces
We shall present various aspects of the minimization of functionals for immersion into the spheres of surfaces under constrained conformal class. We will focus in particular on the variations of the Willmore and the area functional in the class of weak conformal immersions of given Riemann surfaces. We will in particular give a characterization of riemann tori into S3 minimizing locally the conformal volume. |
17:45 Uhr | Ben Sharp (Imperial) | Compactness theorems for minimal hypersurfaces with bounded index
I will present a new compactness theorem for minimal hypersurfaces embedded in a closed Riemannian manifold N^{n+1} with n<7. When n=2 and N has positive Ricci curvature, Choi and Schoen proved that a sequence of minimal hypersurfaces with bounded genus converges smoothly and graphically to some minimal limit. A corollary of our main theorem recovers the result of Choi-Schoen and extends this appropriately for all n<7. |