Geometric Analysis and Topology Seminar

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Compactness and Blow-Up Phenomena for Constant Scalar Curvature Metrics in High Dimensions

Speaker: Rick Schoen

Location: Warren Weaver Hall 202

Date: Friday, October 30, 2009, 11 a.m.

Synopsis:

While the existence of minimizing metrics of constant scalar curvature in a conformal class has been known since the middle 1980's, the question of whether the space of all constant scalar curvature metrics in a conformal class is compact (in other words whether there are suitable estimates on solutions) was not fully resolved. We will describe work over the past few years which shows that the estimates are true for manifolds of dimension at most 24, but sometimes fail in higher dimensions.