THE LONG-TIME EXISTENCE AND CONVERGENCE OF THE CR YAMABE FLOW

In this paper, we prove the long-time existence of the CR Yamabe flow on the compact strictly pseudoconvex CR manifold with positive CR invariant. We also prove the convergence of the CR Yamabe flow on the sphere by proving that: the contact form which is pointwise conformal to the standard contact form on the sphere converges exponentially to a contact form of constant pseudo-Hermitian sectional curvature. We also show that the eigenvalues of some geometric operators are non-decreasing under the unnormalized CR Yamabe flow provided that the pseudo-Hermitian scalar curvature satisfies certain conditions.