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A rigidity theorem for holomorphic disks in Teichmüller space


Author: Hideki Miyachi
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
Published electronically: February 16, 2015
MathSciNet review: 3336619
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2015-12488-4
Keywords: Teichm\"uller space, Teichm\"uller distance, Kobayashi distance, pseudoconvex domains
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.
Dedicated: This paper is dedicated to Professor Hiroshige Shiga on the occasion of his 60th birthday.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2015 American Mathematical Society

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