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The exponential convergence of the CR Yamabe flow

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Abstract

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

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11571304).

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Author notes

  1. Kunbo Wang

    Present address: Current address: College of Sciences, China Jiliang University, Hangzhou, 310018, China

Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Weimin Sheng & Kunbo Wang

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  1. Weimin Sheng
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  2. Kunbo Wang
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Correspondence to Kunbo Wang.

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Sheng, W., Wang, K. The exponential convergence of the CR Yamabe flow. Sci. China Math. 63, 979–992 (2020). https://doi.org/10.1007/s11425-017-9365-7

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  • DOI: https://doi.org/10.1007/s11425-017-9365-7

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