Event

Talk
Nonlinear evolution by mean curvature and isoperimetric inequalities
Dr. Felix Schulze (FU Berlin)
17 Jul 2006, 14:00 – 15:00

Evolving smooth, compact hypersurfaces in R^n+1 with normal speed equal to a positive power k of the mean curvature improves a certain 'isoperimetric difference' for k >= n-1. As singularities may develop before the volume goes to zero, we develop a weak level-set formulation for such flows and show that the above monotonicity is still valid. This proves the isoperimetric inequality for n <= 7. Extending this to complete, simply connected 3- dimensional manifolds with nonpositive sectional curvature, we give a new proof for the Euclidean isoperimetric inequality on such manifolds.

Related to:

• Felix Schulze