%0 Journal Article
%T Holomorphic Mappings between Hyperquadrics with Small Signature Difference
%A M. Salah Baouendi
%A Peter Ebenfelt
%A Xiaojun Huang
%J Mathematics
%D 2009
%I arXiv
%X In this paper, we study holomorphic mappings sending a hyperquadric of signature $\ell$ in $\bC^n$ into a hyperquadric of signature $\ell'$ in $\bC^N$. We show (Theorem \ref{main}) that if the signature difference $\ell'-\ell$ is not too large, then the mapping can be normalized by automorphisms of the target hyperquadric to a particularly simple form and, in particular, the image of the mapping is contained in a complex plane of a dimension that depends only on $\ell$ and $\ell'$, and not on the target dimension $N$. We also prove a Hopf Lemma type result (Theorem \ref{main2}) for such mappings.
%U http://arxiv.org/abs/0906.1235v1