English

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 QQ'-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}
}

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22 pages