CR Nirenberg problem and zero Wester scalar curvature

Abstract

In this paper, we study the prescribing Webster scalar curvature problem on strictly pseudoconvex CR manifolds of real dimension \(2n+1\). First, we study the CR Nirenberg problem and prove some existence results. Second, we provide the existence and a positive lower bound for a solution of the CR Yamabe problem with zero Webster scalar curvature on noncompact complete manifolds.

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Acknowledgements

Kim was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2011-0025674). Ho was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019041021), and by Korea Institute for Advanced Study (KIAS) Grant funded by the Korea government (MSIP).

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Correspondence to Seongtag Kim.

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Ho, P.T., Kim, S. CR Nirenberg problem and zero Wester scalar curvature. Ann Glob Anal Geom (2020). https://doi.org/10.1007/s10455-020-09721-w

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Keywords

  • CR manifold
  • CR Yamabe problem
  • Webster scalar curvature
  • CR Nirenberg problem

Mathematics Subject Classification

  • Primary 32V05
  • Secondary 53C21