GÖRAN GUSTAFSSON Lectures in Mathematics April 6-8, 2016 KTH, Stockholm
Gerhard Huisken
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Abstracts Lecture 1: Geometric heat equations
Wednesday, April 6, 1.15-2.15 pm Starting from the linear heat equation the lecture introduces geometric heat equations such as the curve shortening flow, the mean curvature flow of hypersurfaces and the Ricci flow of Riemannian metrics. It is shown how these quasi-linear parabolic systems can be used to deform geometric objects into more uniform, recognizable shapes, leading to classification results such as the proof of the Poincaré conjecture. Particular emphasis will be on the necessary interplay between geometric concepts and analytical estimates. Coffee is served between 12.45 and 1.15 outside the lecture hall.
Lecture 2: Mean curvature flow with surgery
Thursday, April 7, 1.15-2.15 pm
Lecture 3: Embedded mean-convex hypersurfaces in 3-manifolds
Friday, April 8, 10.15-11.15 am The lecture describes recent work with S. Brendle on embedded surfaces of positive mean curvature that move by mean curvature in a general Riemannian 3-manifold. We prove a general long-time existence and convergence result for a flow interrupted only by finitely many surgeries. As an application we construct canonical sweep-outs by 2-surfaces for asymptotically flat 3-manifolds arising as time-slices in Lorentzian manifolds that model isolated gravitating systems in General Relativity.
2016-02-11 |