17:45 Uhr | Andrea Mondino | The Willmore functional in Riemannian manifolds Given an immersed surface $\Sigma$ in the Euclidean space, the Willmore functional is defined as the $L^2$ norm of the mean curvature. If the surface is immeresd in a Riemannian manifold there are several natural generalizations: the $L^2$ curvature functionals. The topic as links with general realtivity (the Hawking mass), Biology (Hellfrich energy), string theory (Polyakov extrinsic action), etc. After introducing the various functionals and discussing their properties, I will give a panoramic view of the different techniques and the recent results obtained in various collaboration with Kuwert, Rivière and Schygulla. |