The strong rigidity of locally symmetric complex manifolds of rank one and finite volume

Jrgen Jost Shing-Tung Yau

Complex Variables and Complex Analysis mathscidoc:1912.43568

Mathematische Annalen, 275, (2), 291-304, 1986.6
Rigidity question have attracted much interest in the past. In the compact case, we have the famous work of Calabi and Vesentini [3] and Mostow [17]. Whereas Calabi and Vesentini proved a local version, namely that compact quotients of bounded symmetric domains admit no nontrivial deformations in case the domain is irreducible and of complex dimension at least 2, Mostow proved a global rigidity result, at the expense, however, of working only within the class of quotients of symmetric domains. Mostow's work is based on quasiconformal mappings. A different analytic approach was recently undertaken by Siu [22]. If M is a compact K~ ihler manifold diffeomorphic (or, more generally, homotopically equivalent) to a quotient N of an irreducible bounded symmetric domain, he studied a harmonic homotopy equivalence the existence of which is assured by the theorem of EeUs and Sampson, and demonstrated that
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@inproceedings{jrgen1986the,
  title={The strong rigidity of locally symmetric complex manifolds of rank one and finite volume},
  author={Jrgen Jost, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204110908736132},
  booktitle={Mathematische Annalen},
  volume={275},
  number={2},
  pages={291-304},
  year={1986},
}
Jrgen Jost, and Shing-Tung Yau. The strong rigidity of locally symmetric complex manifolds of rank one and finite volume. 1986. Vol. 275. In Mathematische Annalen. pp.291-304. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204110908736132.
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