Nonconstant cr morphisms between compact strongly pseudoconvex cr manifolds and ´etale covering between resolutions of isolated singularities

Yu-Chao Tu Princeton University Stephen S.-T. Yau Tsinghua University Huaiqing Zuo Tsinghua University

Differential Geometry mathscidoc:1609.10334

Distinguished Paper Award in 2017

Journal of Differential Geometry, 95, (2), 337-354, 2013
Strongly pseudoconvex CR manifolds are boundaries of Stein varieties with isolated normal singularities.We prove that any nonconstant CR morphism between two (2n.1)-dimensional strongly pseudoconvex CR manifolds lying in an n-dimensional Stein variety with isolated singularities are necessarily a CR biholomorphism. As a corollary, we prove that any nonconstant self map of (2n . 1)-dimensional strongly pseudoconvex CR manifold is a CR automorphism. We also prove that a finite ′etale covering map between two resolutions of isolated normal singularities must be an isomorphism.
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@inproceedings{yu-chao2013nonconstant,
  title={NONCONSTANT CR MORPHISMS BETWEEN COMPACT STRONGLY PSEUDOCONVEX CR MANIFOLDS AND ´ETALE COVERING BETWEEN RESOLUTIONS OF ISOLATED SINGULARITIES},
  author={Yu-Chao Tu, Stephen S.-T. Yau, and Huaiqing Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914082836195125996},
  booktitle={Journal of Differential Geometry},
  volume={95},
  number={2},
  pages={337-354},
  year={2013},
}
Yu-Chao Tu, Stephen S.-T. Yau, and Huaiqing Zuo. NONCONSTANT CR MORPHISMS BETWEEN COMPACT STRONGLY PSEUDOCONVEX CR MANIFOLDS AND ´ETALE COVERING BETWEEN RESOLUTIONS OF ISOLATED SINGULARITIES. 2013. Vol. 95. In Journal of Differential Geometry. pp.337-354. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914082836195125996.
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