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Geometric Flows and Geometric Operators

seminar: Monotone volume formulas for geometric flows

speaker: Reto Mueller (Scuola Normale Superiore, Pisa)

abstract: We consider geometric flows, where a metric evolves by \partial_t g = -2 S for some symetric two-tensor S. For these flows we define forwards and backwards reduced volume quantities in the spirit of Perelman's backwards reduced volume for the Ricci flow. We show that if S satisfies a Harnack type inequality along the flow these volume quantites are monotone. This result implies new monotonicity formulas for flows like Bernhard List's extended Ricci flow system or the mean curvature flow in certain Lorentzian manifolds.

timetable:
Wed 13 May, 17:00 - 18:00, Sala Conferenze Centro De Giorgi
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