Asian Journal of Mathematics

Volume 22 (2018)

Number 4

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

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n4.a7

Authors

Ming Xiao (Department of Mathematics, University of California at San Diego)

Yuan Yuan (Department of Mathematics, Syracuse University, Syracuse, New York, U.S.A.)

Abstract

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.

Keywords

Bergman metric, classical domain, holomorphic isometry, proper map

2010 Mathematics Subject Classification

32H02, 32M15

Full Text (PDF format)

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