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arXiv · 1201.6440

On the Third Gap for Proper Holomorphic Maps between Balls

Xiaojun Huang·Shanyu Ji·Wanke Yin
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Abstract

In this paper, we study the gap rigidity phenomenon for proper holomorphic maps between balls of different dimension. We show that any $F\in prop_3({\mathbb{B}}^n, {\mathbb{B}} ^N)$, with $3n<N\leq 4n-7$ and $n\geq 7$, is equivalent to a map of the form $(G,0)$ with $G\in Rat ({\mathbb{B}}^n,{\mathbb{B}}^{3n})$. 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.

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Xiaojun Huang, Shanyu Ji, Wanke Yin. 2014-10-14. On the Third Gap for Proper Holomorphic Maps between Balls. https://arxiv.org/abs/1201.6440

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