Asian Journal of Mathematics

Volume 22 (2018)

Number 3

Special issue in honor of Ngaiming Mok (2 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

Upper boundary points of the gap intervals for rational maps between balls

Pages: 493 – 506



Shanyu Ji (Department of Mathematics, University of Houston, Texas, U.S.A.)

Wanke Yin (School of Mathematics and Statistics, Wuhan University, Hubei, China)


The paper focuses on the study of rational proper holomorphic maps from $\mathbb{B}^n$ to $\mathbb{B}^N$. We classify these maps when $N$ is the upper boundary point of the gap interval $I_k , k \leq n-2$ and the geometric rank of the map is $k$.


proper holomorphic maps, holomorphic classification, geometric rank, Chern–Moser equation

2010 Mathematics Subject Classification


Both authors are supported in part by NSFC-11571260. The second author is also supported in part by NSFC-11722110.

Received 19 May 2016

Accepted 12 June 2017

Published 8 August 2018