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

abstract

• 2016, Mathematica Josephina, Inc. Let M CN and MCN 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.

authors

• Mir, Nordine

published proceedings

• JOURNAL OF GEOMETRIC ANALYSIS

author list (cited authors)

• Mir, N.

citation count

• 8

complete list of authors

• Mir, Nordine

publication date

• July 2017

publisher

• Springer Nature  Publisher

published in

• Journal of Geometric Analysis  Journal

keywords

• Analyticity
• Cr Map
• Holomorphic Deformation

Digital Object Identifier (DOI)

• 10.1007/s12220-016-9745-4

start page

• 1920

end page

• 1939

volume

• 27

issue

• 3

URL

• http://dx.doi.org/10.1007/s12220-016-9745-4