Kohn-rossi cohomology and nonexistence of cr morphisms between compact strongly pseudoconvex cr manifolds

Stephen S.-T.Yau Tsinghua University Huaiqing Zuo Tsinghua University

mathscidoc:1906.01004

j. differential geometry, 111, 567-580, 2019
One of the fundamental questions in CR geometry is: Given two strongly pseudoconvex CR manifolds X1 and X2 of dimension 2n􀀀 1, is there a non-constant CR morphism between them? In this paper, we use Kohn{Rossi cohomology to show the non-existence of non-constant CR morphism between such two CR manifolds. Speci cally, if dimHp;q KR(X1) < dimHp;q KR(X2) for any (p; q) with 1  q  n 􀀀 2, then there is no non-constant CR morphism from X1 to X2.
KOHN{ROSSI COHOMOLOGY
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@inproceedings{stephen2019kohn-rossi,
  title={KOHN-ROSSI COHOMOLOGY AND NONEXISTENCE OF CR MORPHISMS BETWEEN COMPACT STRONGLY PSEUDOCONVEX CR MANIFOLDS},
  author={Stephen S.-T.Yau, and Huaiqing Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190626024346701074362},
  booktitle={j. differential geometry},
  volume={111},
  pages={567-580},
  year={2019},
}
Stephen S.-T.Yau, and Huaiqing Zuo. KOHN-ROSSI COHOMOLOGY AND NONEXISTENCE OF CR MORPHISMS BETWEEN COMPACT STRONGLY PSEUDOCONVEX CR MANIFOLDS. 2019. Vol. 111. In j. differential geometry. pp.567-580. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190626024346701074362.
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