Abstract
This seminar concerns a class of flow equations for immersed hypersurfaces, modelled on the well-known mean curvature flow. The flows in this class share much of the qualitative behaviour of the mean curvature flow, but are in general fully nonlinear; this compiicates some parts of their analysis. Other calculations are clarified by the general setting. I will present some results on the behaviour of convex hypersurfaces under these flows, which extend work on specific flows by Huisken (Hul), Tso (Tl) and Chow (Cl-2). Also new is a Harnack inequality for solutions of very general flows; this generalises results of Hamilton (Hal) and Chow (C3). Flows of this kind have some applications in geometry; for such purposes the mean curvature flow is not always the best candidate - I will describe an example which applies to manifolds of non-negative sectional curvature.
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