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Schwarz Type Lemmas for Pseudo-Hermitian Manifolds

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In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds. These maps include the CR maps and the transversally holomorphic maps. In terms of some sub-Laplacian or Hessian type Bochner formulas, and comparison theorems in the pseudo-Hermitian version, we are able to establish several Schwarz type results for both the CR maps and the transversally holomorphic maps between pseudo-Hermitian manifolds. Finally, we also discuss the CR hyperbolicity problem for pseudo-Hermitian manifolds.

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Acknowledgements

We thank the anonymous referees of this paper for their careful reading and helpful comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Yuxin Dong & Weike Yu

  2. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China

    Yibin Ren

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  1. Yuxin Dong
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  2. Yibin Ren
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  3. Weike Yu
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Correspondence to Weike Yu.

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Y. Dong: supported by NSFC Grant No. 11771087, and LMNS, Fudan. Y. Ren: supported by NSFC Grant No. 11801517.

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Dong, Y., Ren, Y. & Yu, W. Schwarz Type Lemmas for Pseudo-Hermitian Manifolds. J Geom Anal 31, 3161–3195 (2021). https://doi.org/10.1007/s12220-020-00389-z

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