Asian Journal of Mathematics
Volume 22 (2018)
Special issue in honor of Ngaiming Mok (3 of 3)
Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University
Complexity of holomorphic maps from the complex unit ball to classical domains
Pages: 729 – 760
We study the complexity of holomorphic isometries and proper maps from the complex unit ball to type IV classical domains. We investigate on degree estimates of holomorphic isometries and holomorphic maps with minimum target dimension. We also construct a real-parameter family of mutually inequivalent holomorphic isometries from the unit ball to type IV domains. We also provide examples of non-isometric proper holomorphic maps from the complex unit ball to classical domains.
Bergman metric, classical domain, holomorphic isometry, proper map
2010 Mathematics Subject Classification
Ming Xiao was supported in part by National Science Foundation grant DMS-1800549.
Yuan Yuan was supported in part by National Science Foundation grant DMS-1412384 and the seed grant program at Syracuse University.
Received 11 October 2016
Accepted 7 June 2017
Published 20 September 2018