On the Third Gap for Proper Holomorphic Maps between Balls

Abstract

In this paper, we study the gap rigidity phenomenon for proper holomorphic maps between balls of different dimension. We show that any $F\in pro{p}_3({\mathbb{B}}^n,{\mathbb{B}}^N)$, with $3n<N\le 4n-7$ and $n\ge 7$, 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.

Appeared in Math. Ann. in 2014

References in corpus (1)

• Complexity results for CR mappings between spheres

Cited by in corpus (1)

• CR and Holomorphic Embeddings and Pseudo-conformally Flat Metrics