In this paper we study contact forms on the three-dimensional Heisenberg manifold with its standard CR structure. We discover that the Q0-curvature, introduced by Branson, Fontana and Morpurgo  on the CR three-sphere and then generalized to any pseudo-Einstein CR three-manifold by Case and Yang , controls the isoperimetric inequality on such a CR-manifold. As the first and important step to show this, we prove that the nonnegative Webster curvature at infinity implies that the metric is normal, which is analogous to the behavior on a Riemannian four-manifold.
|Number of pages
|Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
|Published - 2018
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Mathematics (miscellaneous)