Geometric flows and their singularities
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Thu, 16/02/2012 12:30 |
Reto Müller (Imperial College, London) |
OxPDE Lunchtime Seminar  |
Gibson 1st Floor SR |
| In this talk, we first study the Mean Curvature Flow, an evolution equation for submanifolds of some Euclidean space. We review a famous monotonicity formula of Huisken and its application to classifying so-called Type I singularities. Then, we discuss the Ricci Flow, which might be seen as the intrinsic analog of the Mean Curvature Flow for abstract Riemannian manifolds. We explain how Huisken's classification of Type I singularities can be adopted to this intrinsic setting, using monotone quantities found by Perelman. | |||