Holomorphic Deformations of Real-Analytic CR Maps and Analytic Regularity of CR Mappings

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3 Citations (Scopus)

Abstract

Let (Formula presented.) and (Formula presented.) 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 (Formula presented.) 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.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalJournal of Geometric Analysis
DOIs
Publication statusAccepted/In press - 27 Sep 2016

Fingerprint

CR Mappings
Regularity
CR-submanifold
Subset
Analyticity
Nonexistence
Generalise
Integer
Necessary
Sufficient Conditions

Keywords

  • Analyticity
  • CR map
  • Holomorphic deformation

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

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AB - Let (Formula presented.) and (Formula presented.) 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 (Formula presented.) 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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