A generalization of Gromov's almost flat manifold theorem
Dienstag, 5.11.13, 16:00-17:00, Raum 404, Eckerstr. 1
Almost flat manifolds are the solutions of bounded size perturbations of the equation Sec = 0 (Sec is the sectional curvature). In a celebrated theorem, Gromov proved that the presence of an almost flat metric implies a precise topological description of the underlying manifold.\n\nDuring this talk we will explain how, under lower sectional curvature bounds, to impose an L1-pinching condition on the curvature is surprisingly rigid, leading indeed to the same conclusion as in Gromov's theorem under more relaxed curvature conditions (in particular, so weak that we are not allowed to use Ricci flow in the proof). We will describe which alternative techniques lead us to a successful proof, ans this will be sketched in detail. This is a joint work with B. Wilking.\n
Minimal hypersurfaces in manifolds with nonnegative Ricci curvature
Dienstag, 12.11.13, 16:00-17:00, Raum 404, Eckerstr. 1
In this talk, I would like to discuss minimal hypersurfaces in complete manifolds with nonnegative Ricci curvature and Euclidean volume growth. The existence of area minimizing hypersurfaces is strongly influenced by Ricci curvature of ambient manifolds, where our model spaces are the Euclidean cones over spheres of radius less than 1. Moreover, I would like to study minimal graphs in product manifolds, and talk about gradient estimates and Liouville type theorems for minimal graphic functions.\n\n
The closure theorem for integer rectifiable currents
Dienstag, 7.1.14, 16:15-17:15, Raum 404, Eckerstr. 1
The closure theorem for integer rectifiable currents
Dienstag, 14.1.14, 16:15-17:15, Raum 404, Eckerstr. 1
A Kinematic Formula for Hypersurfaces
Dienstag, 21.1.14, 16:15-17:15, Raum 404, Eckerstr. 1
The closure theorem for integer rectifiable currents
Dienstag, 21.1.14, 17:10-18:10, Raum 404, Eckerstr. 1
The compactness theorem for area minimizing currents
Dienstag, 28.1.14, 16:15-17:15, Raum 404, Eckerstr. 1