Holomorphic Deformations of Real-Analytic CR Maps and Analytic Regularity of CR Mappings
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© 2016, Mathematica Josephina, Inc. Let M⊂ CN and M′⊂CN′ be real-analytic CR submanifolds, with M minimal. We provide a new sufficient condition, that happens to be also essentially necessary, for all sufficiently smooth CR maps h: U→ M′ defined on a connected open subset of M and of rank larger than a prescribed integer r to be real-analytic on a dense open subset of U. This condition corresponds to the nonexistence of nontrivial holomorphic deformations of germs of real-analytic CR mappings whose rank is larger than r. As a consequence, we obtain several new results about analyticity of CR mappings that, at the same time, generalize and unify a number of previous existing ones.
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