PDE Seminar: Schulze -- Nonlinear evolution of hypersurfaces and geometric inequalities

  Felix Schulze, Freie Universitat Berlin

  New time! 3.30pm-4.30pm, Friday 26th September, Room 707A  

  Abstract: In recent years, evolving hypersurfaces with normal speed  
equal to a function of its principal curvatures has been applied in  
several cases to prove new geometric inequalities. In this talk we  
will describe some of these results and discuss a recent result of the  
speaker, how a weak level-set formulation of the flow with speed equal  
to a positive power of the mean curvature can be used to give a new  
proof of the isoperimetric inequality in R^n up to dimension 8. We  
also show how this technique can be extended to complete, simply  
connected 3-manifolds with nonpositive sectional curvature to yield a  
new proof of the Euclidean isoperimetric inequality on such manifolds.