Real Analytic Sets in Complex Spaces and CR maps

2006/12/28 by Shafikov, Rasul
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0612829

Abstract

If R is a real analytic set in \Cⁿ (viewed as \R²ⁿ), then for any point p∈ R there is a uniquely defined germ X_p of the smallest complex analytic variety which contains R_p, the germ of R at p. It is shown that if R is irreducible of constant dimension, then the function p→dim X_p is constant on a dense open subset of R. As an application it is proved that a continuous map from a real analytic CR manifold M into \C^N which is CR on some open subset of M and whose graph is a real analytic set in M× \C^N is necessarily CR everywhere on M.

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