## A rigidity theorem for holomorphic disks in Teichmüller space

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## Abstract:

In this paper, we discuss a rigidity property for holomorphic disks in Teichmüller space. In fact, we give an improvement of Tanigawa’s rigidity theorem. We will also treat the rigidity property of holomorphic disks for complex manifolds. We observe the rigidity property is valid for bounded strictly pseudoconvex domains with $C^{2}$-boundaries, but the rigidity property does not hold for product manifolds.## References

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## Additional Information

**Hideki Miyachi**- Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka 560-0043, Japan
- MR Author ID: 650573
- Received by editor(s): December 26, 2013
- Received by editor(s) in revised form: January 3, 2014, and February 8, 2014
- Published electronically: February 16, 2015
- Additional Notes: The author was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 21540177.
- Communicated by: Franc Forstneric
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**143**(2015), 2949-2957 - MSC (2010): Primary 32G15; Secondary 32F10, 32T15, 32E35
- DOI: https://doi.org/10.1090/S0002-9939-2015-12488-4
- MathSciNet review: 3336619

Dedicated: This paper is dedicated to Professor Hiroshige Shiga on the occasion of his 60th birthday.