Analytic Continuation of Holomorphic Correspondences and Equivalence of Domains in ${\mathbb C}^n$

Details Analytic Continuation of Holomorphic Correspondences and Equivalence of Domains in ${\mathbb C}^n$ Analytic Continuation of Holomorphic Correspondences and Equivalence of Domains in ${\mathbb C}^n$

2002-01-25

arxiv.org/abs/math/0201247v1

Mathematics

Complex Variables

17 pages

Scientific paper

10.1007/s00222-002-0282-3

The following result is proved: Let $D$ and $D'$ be bounded domains in $\mathbb C^n$, $\partial D$ is smooth, real-analytic, simply connected, and $\partial D'$ is connected, smooth, real-algebraic. Then there exists a proper holomorphic correspondence $f:D\to D'$ if and only if $\partial D$ and $\partial D'$ a locally CR-equivalent. This leads to a characterization of the equivalence relationship between bounded domains in $\mathbb C^n$ modulo proper holomorphic correspondences in terms of CR-equivalence of their boundaries.

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