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arXiv · 1611.03564

Isoperimetric inequality on CR-manifolds with nonnegative $Q'$-curvature

Yi Wang·Paul Yang
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Abstract

In this paper, we study contact forms on the three- dimensional Heisenberg manifold with its standard CR structure. We discover that the $Q'$-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.

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Yi Wang, Paul Yang. 2016-11-11. Isoperimetric inequality on CR-manifolds with nonnegative $Q'$-curvature. https://arxiv.org/abs/1611.03564

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