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Geometric Analysis and Partial Differential Equations Seminar
April 24, 2014 @ 10:30 am - 11:30 pm
Prof. Miles Simon (Otto-von-Guericke Universitaet)
Local estimates for Ricci-flow in two dimensions
In all dimensions G. Perelman proved the following. If an open ball contained in a manifold is ‘almost Euclidean’, then one can prove estimates on how compactly contained sub-regions of this ball evolve under Ricci flow. We generalise this result in two dimensions to regions which are not necessarily almost Euclidean. The estimates we obtain depend on the infimum of the curvature within the ball at time zero and the volume of the ball at time zero.