The Yamabe problem on noncompact CR manifolds

Pak Tung Ho and Seongtag Kim

Vol. 285 (2016), No. 2, 375–391

DOI: 10.2140/pjm.2016.285.375

Abstract

Let $\left(M,\theta \right)$ be a noncompact complete strictly pseudoconvex CR manifold of real dimension $2n+1\ge 3$ with positive Webster scalar curvature. We show that there exists a conformal contact form $\tilde{\theta }=u^{2∕n}\theta$ with positive constant Webster scalar curvature if the CR-Yamabe invariant $Y\left(M,\theta \right)$ of $\left(M,\theta \right)$ is positive and strictly less than the CR-Yamabe invariant at infinity $\left[t\right]\overline{Y\left(M,\theta \right)}$.

Keywords

CR manifolds, CR Yamabe problem, Webster scalar curvature, conformal changes, noncompact complete manifolds

Mathematical Subject Classification 2010

Primary: 32V20, 53C21

Secondary: 32V05, 58J05

Milestones

Received: 15 February 2016

Revised: 18 April 2016

Accepted: 31 May 2016

Published: 21 November 2016