Isoperimetric inequality on CR-manifolds with nonnegative $Q'$-curvature
Differential Geometry
2016-11-14 v1
Abstract
In this paper, we study contact forms on the three- dimensional Heisenberg manifold with its standard CR structure. We discover that the -curvature, introduced by Branson, Fontana and Morpurgo [BFM13] on the CR three-sphere and then generalized to any pseudo-Einstein CR three manifold by Case and Yang [CY95], controls the isoperimetric inequality on such a CR-manifold. To show this, we first prove that the nonnegative Webster curvature at infinity deduces that the metric is normal, which is analogous to the behavior on a Riemannian four-manifold.
Keywords
Cite
@article{arxiv.1611.03564,
title = {Isoperimetric inequality on CR-manifolds with nonnegative $Q'$-curvature},
author = {Yi Wang and Paul Yang},
journal= {arXiv preprint arXiv:1611.03564},
year = {2016}
}
Comments
22 pages