Mathematics Colloquium

The inverse mean curvature flow is an evolution of hypersurfaces where the normal velocity is the reciprocal of mean curvature. In this talk we will give an introductory overview of this subject. We will begin with the origin in mathematical relativity, then introduce the notion of weak flow due to Huisken and Ilmanen (which played a central role in recent theories). Finally, we will discuss some recent developments and connections to other areas such as scalar curvature geometry and nonlinear potential theory.