The Journal of Geometric Analysis

, Volume 2, Issue 4, pp 381–387 | Cite as

Local behaviors of CR homeomorphisms between hypersurfaces

  • Zaifei Ye


We show that if a CR homeomorphism can be holomorphically extended to a neighborhood of a nonminimal point (in Tumanov's sense), then the extended map is proper, and, near a minimal point, the holomorphic extension is biholomorphic in a neighborhood of the point.

Math Subject Classification (1985 Revision)

Primary: 32D15 Secondary: 32A07 

Key Words and Phrases

CR mappings proper map varieties 


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  1. [Bel] Bell, S. Local regularity of CR homeomorphisms. Duke Math. J.57, 295–300 (1988).MATHCrossRefMathSciNetGoogle Scholar
  2. [BR] Baouendi, S., and Rothschild, L. P. A generalized complex Hopf lemma and its applications to CR mappings. Preprint, University of California at San Diego.Google Scholar
  3. [Chr] Chirka, E. M. Complex analytic set. Dordrecht: Kluwer 1989.Google Scholar
  4. [DF] Diederich, K., and Fornness, J. Pseudoconvex domains: Existence of Stein neighborhoods. Duke Math. J.44, 641–662 (1977).MATHCrossRefMathSciNetGoogle Scholar
  5. [P] Pinchuk, S. CR transformations of real manifolds in ℂn. Preprint, Max-Planck Institute, Germany.Google Scholar
  6. [Trp] Trepreau, J. M. Sur le prolongement holomorphe des fonctions CR definies sur une hypersurface reelle de classeC 2 dans ℂn. Invent. Math.83, 583–592 (1986).MATHCrossRefMathSciNetGoogle Scholar
  7. [Tum] Tumanov, A. E. Extending CR functions on manifolds of finite type to a wedge. Math. Sbornik136, 128–139 (1989).MathSciNetGoogle Scholar

Copyright information

© Mathematica Josephina, Inc. 1992

Authors and Affiliations

  • Zaifei Ye
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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