On proper holomorphic maps between bounded symmetric domains
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- by Shan Tai Chan PDF
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Abstract:
We study proper holomorphic maps between bounded symmetric domains $D$ and $\Omega$. In particular, when $D$ and $\Omega$ are of the same rank $\ge 2$ such that all irreducible factors of $D$ are of rank $\ge 2$, we prove that any proper holomorphic map from $D$ to $\Omega$ is a totally geodesic holomorphic isometric embedding with respect to certain canonical Kähler metrics of $D$ and $\Omega$. We also obtain some results regarding holomorphic maps $F:D\to \Omega$ which map minimal disks of $D$ properly into rank-$1$ characteristic symmetric subspaces of $\Omega$. On the other hand, we obtain new rigidity results regarding semi-product proper holomorphic maps between $D$ and $\Omega$ under a certain rank condition on $D$ and $\Omega$.References
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Additional Information
- Shan Tai Chan
- Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
- MR Author ID: 1132275
- Email: mastchan@hku.hk
- Received by editor(s): January 9, 2019
- Received by editor(s) in revised form: April 4, 2019
- Published electronically: July 8, 2019
- Communicated by: Filippo Bracci
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 173-184
- MSC (2010): Primary 32M15, 53C55, 53C42
- DOI: https://doi.org/10.1090/proc/14657
- MathSciNet review: 4042840