Tuesday, February 16, 2021 - 13:00

### Abstract or Additional Information

The evolution of hypersurfaces in a Riemannian manifold along its mean curvature vector is governed by a quasilinear parabolic system that exhibits smoothing behavior and singularity formation at the same time since the evolution of the geometry is governed by a non-linear reaction diffusion system. The lecture explains how for embedded 2-surfaces of positive mean curvature in general ambient manifolds long-time solutions can be constructed that contain finitely many surgeries near singular regions. Finally we discuss applications in Geometry and General Relativity.