AI 中文总结
本文证明了具有通有退化CR高斯映射的球内全纯映射在自同构复合下等价于Veronese映射与零映射的直和，解决了黄晓军提出的问题。
AI 中文摘要
设$n$和$N$为满足$2\leq n<N$的整数，并设$F:\mathbb{B}^n\to\mathbb{B}^N$为允许$C^{N-n+1}$-光滑延拓到边界的全纯映射。我们证明，如果其边界限制的CR高斯映射是通有退化的，则$F$在源球和目标球的自同构复合下，全纯等价于$V_m\oplus 0$，其中$m$为正整数，$V_m(z)=\big(\sqrt{\frac{m!}{\alpha!}} z^\alpha\big)_{|\alpha|=m}$为$m$次Veronese映射。这解决了黄晓军提出的一个问题。
英文摘要
Let $n$ and $N$ be integers with $2\leq n<N$, and let $F:\mathbb{B}^n\to\mathbb{B}^N$ be a proper holomorphic map that admits a $C^{N-n+1}$-smooth extension to the boundary. We prove that if the CR Gauss map of its boundary restriction is generically degenerate, then $F$ is holomorphically equivalent, under composition with automorphisms of the source and target balls, to $V_m\oplus 0$ for some positive integer $m$, where $ V_m(z)=\big(\sqrt{\frac{m!}{α!}} z^α\big)_{|α|=m} $ is the degree-$m$ Veronese map. This resolves a problem posed by Xiaojun Huang.
Comments28 pages. Comments are welcome
