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Holomorphic extension of meromorphic mappings along real analytic hypersurfaces

  • Ozcan YaziciEmail author
Article
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Abstract

Let \(M\subset {\mathbb {C}}^n\) be a real analytic hypersurface, \(M'\subset {\mathbb {C}}^N\)\((N\ge n)\) be a strongly pseudoconvex real algebraic hypersurface of the special form, and F be a meromorphic mapping in a neighborhood of a point \(p\in M\) which is holomorphic in one side of M. Assuming some additional conditions for the mapping F on the hypersurface M, we proved that F has a holomorphic extension to p. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensions.

Keywords

Meromorphic mappings Real analytic hypersurfaces Holomorphic extension 

Mathematics Subject Classification

32D15 32H04 32H40 

Notes

Acknowledgements

I am grateful to Nordine Mir for his suggestion to work on this problem and for useful discussions on this subject. I would like to thank the referee for his/her remarks and suggestions which helped to improve the presentation of the paper. The author is supported by TÜBİTAK 2232 Proj. No. 117C037.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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