Holomorphic mappings between hyperquadrics with small signature difference

M. Salah Baouendi, Peter Ebenfelt, Xiaojun Huang

Research output: Contribution to journalArticlepeer-review

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Abstract

In this paper, we study holomorphic mappings sending a hyperquadric of signature ℓ' in ℂn into a hyperquadric of signature ℓ' in ℂN.We show (Theorem 1.1) that if the signature difference ℓ'-ℓ 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 ℓ and ℓ', and not on the target dimension N. We also prove a Hopf Lemma type result (Theorem 1.3) for such mappings.

Original languageEnglish (US)
Pages (from-to)1633-1661
Number of pages29
JournalAmerican Journal of Mathematics
Volume133
Issue number6
DOIs
StatePublished - Dec 2011
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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