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Veranstaltung

Vortragsveranstaltung
SFB-Seminartag
Dr. Schulze, Dr. Pankrashkin
17.7.2006, 14:00 Uhr – 17:00 Uhr

Programm

Vortrag
Nonlinear evolution by mean curvature and isoperimetric inequalities
Dr. Felix Schulze (FU Berlin)
17.7.2006, 14:00 Uhr – 15:00 Uhr

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.

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Vortragsveranstaltungen 2006