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

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. ÌýI also show how these results lead to the classification of minimizers of various Sobolev-type inequalities. ÌýIn 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.