Seminar: Uniqueness Results on a geometric PDE in Riemannian and CR Geometry Revisited

Seminar| Institute of Mathematical Sciences

Abstract:  We revisit some uniqueness results for a geometric nonlinear PDE related to the scalar curvature in Riemannian geometry and CR geometry. In the Riemannian case we give a new proof of the uniqueness result assuming only a positive lower bound for Ricci curvature. We apply the same principle in the CR case and reconstruct the Jerison-Lee identity in a more general setting. As a consequence, we prove a stronger uniqueness result in the CR case. We also discuss some open problems for further study.

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