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Joint Princeton-Rutgers Seminar on Geometric PDE's

New result on constant Q-curvature metrics 

Yannick Sire, Johns Hopkins University 

Date & time: Wednesday, 16 October 2019 at 1:45PM - 2:45PM

Abstract: In the recent years, several major results have been obtained in the problem of finding a constant Q-curvature metric in a given conformal class in dimensions bigger than 5. This talk will cover new results concerning existence and multiplicity of such metrics. I will first present a rather general geometric approach to prove existence and multiplicity of regular metrics, giving several explicit examples. Then I will move to the case of singular metrics, i.e. complete metrics with constant Q-curvature outside of a closed set. This requires to develop several tools to handle 4th order equations (but applicable actually to higher order ones). I will also provide some explicit examples of such metrics and investigate their multiplicity. I will state open problems as well. 

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