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Properties of squeezing functions and global transformations of bounded domains


Authors: Fusheng Deng, Qi’an Guan and Liyou Zhang
Journal: Trans. Amer. Math. Soc. 368 (2016), 2679-2696
MSC (2010): Primary 32H02, 32F45
DOI: https://doi.org/10.1090/tran/6403
Published electronically: August 19, 2015
MathSciNet review: 3449253
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Abstract: The central purpose of the present paper is to study boundary behaviors of squeezing functions on some bounded domains. We prove that the squeezing function of any strongly pseudoconvex domain tends to 1 near the boundary. In fact, such an estimate is proved for the squeezing function on any bounded domain near its globally strongly convex boundary points. We also study the stability properties of squeezing functions on a sequence of bounded domains, and give some comparisons of intrinsic measures and metrics on bounded domains in terms of squeezing functions. As applications, we give new proofs of several well-known results about geometry of strongly pseudoconvex domains, and prove that all Cartan-Hartogs domains are homogenous regular. Finally, some related problems for further study are proposed.


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Additional Information

Fusheng Deng
Affiliation: School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
Email: fshdeng@ucas.ac.cn

Qi’an Guan
Affiliation: Beijing International Center for Mathematical Research, and School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
Email: guanqian@math.pku.edu.cn

Liyou Zhang
Affiliation: School of Mathematical Sciences, Capital Normal University, Beijing 100048, People’s Republic of China
Email: zhangly@cnu.edu.cn

DOI: https://doi.org/10.1090/tran/6403
Keywords: Squeezing function, homogeneous regular domain, globally strongly convex boundary point
Received by editor(s): April 24, 2013
Received by editor(s) in revised form: January 26, 2014
Published electronically: August 19, 2015
Additional Notes: The authors were partially supported by NSFC grants and BNSF(No.1122010).
Article copyright: © Copyright 2015 American Mathematical Society