The Obata-Vetois argument and its applications

Jeffrey Case, Penn State University
Fine Hall 322

Please note the day and time for this special DGGA Seminar. 

I describe a simplification and generalization of Vetois' Obata-type argument proving uniqueness of conformally Einstein metrics of constant Q-curvature on closed manifolds with positive Yamabe constant.  I also show how these results lead to the classification of minimizers of various Sobolev-type inequalities.  In particular, closed locally symmetric Einstein manifolds with nonnegative Yamabe constant extremize the functional determinant of the conformal Laplacian, answering a question of Branson and Orsted.