The Exponential Convergence of the CR Yamabe Flow

TL;DR

This paper proves that the CR Yamabe flow with zero CR Yamabe invariant converges exponentially to a contact form with flat pseudo-Hermitian scalar curvature, using inequalities to establish long-term existence and convergence.

Contribution

It demonstrates exponential convergence of the CR Yamabe flow under specific conditions, employing novel inequalities for analysis.

Findings

Flow has long-time solution

Converges exponentially to flat scalar curvature

Utilizes CR Poincaré and Gagliardo-Nirenberg inequalities

Abstract

In this paper, we study the CR Yamabe flow with zero CR Yamabe invariant. We use the CR Poincar\'e inequality and a Gagliardo-Nirenberg type interpolation inequality to show that this flow has long time solution and the solution converges to a contact form with flat pseudo-Hermitian scalar curvature exponentially.