國立清華大學 數學系

Abstract I plan to discuss the recently introduced notion of Q-prime curvature equation. A basic result in real dimension three when the underlying CR structure satisfy the two CR invariant conditions: the CR conformal Laplacian is a positive operator, and the CR Paneitz operator is non-negative, then the total Q-prime curvature is bounded from above by that of the standard 3-sphere, and equality holds if and only if the CR structure is biholomorphic to the standard 3-sphere. There are two proofs of this result, first one using the positive mass theorem, while the second one is "elementary"”. I will outline the two different approaches.