Mean curvature flow with surgery

Abstract: 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.

mathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php