About the total Q-prime curvature

Abstract: The Q-prime curvature is a fourth-order local invariant associated to a contact form on a CR structure in dimension three. Its integralis a global invariant of the structure.It is modelled after the Q-curvature of a conformal 4-manifold and enjoys many analogous properties. I will explain some of the known results concerning this invariant. It can be used to characterize domains in the Heisenberg group with finite total Q-prime curvature as the complement of a finite number of points.