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On the Third Gap for Proper Holomorphic Maps between Balls
HUANG Xiaojun 1,JI Shanyu 2 *,YIN Wanke 3 #
1.Department ofMathematics, Rutgers University, New Brunswick, NJ 08903, USA.
2.Department ofMathematics, University of Houston, Houston, TX 77204, USA.
3.School of Mathematics,Wuhan University, WuHan 430072
*Correspondence author
#Submitted by
Subject:
Funding: NSFC(No.10901123), DMS(No.1101481), SRFDP(No.20090141120010), FANEDD(No.201117,ANR-09-BLAN-0422), NSFC(No.11271291)
Opened online:14 December 2012
Accepted by: none
Citation: HUANG Xiaojun,JI Shanyu,YIN Wanke.On the Third Gap for Proper Holomorphic Maps between Balls[OL]. [14 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4500337
 
 
In this paper, we study the gap rigidity phenomenon for proper holomorphic maps between balls of different dimension. We show that any F∈prop3(B n,B N), with 3n<N≤4n-7 and n≥7, is equivalent to a map of the form (G,0) with G∈Rat(B n,B 3n). The main ingredients for the proof of our main theorem are the normal form obtained by Huang-Ji-Xu and a lemma of the first author.
Keywords:Several complex variables; unit ball; proper holomorphic map; gap ridity
 
 
 

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