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[BER1] Algebraicity of holomorphic mappings between real algebraic sets inC n,Acta Math. 177 (1996), 225–273.
[BER2]Baouendi, M. S., Ebenfelt, P. andRothschild, L. P., Local geometric properties of real submanifolds in complex space—a survey,Bull. Amer. Math. Soc 37 (2000), 309–336.
[BHR]Baouendi, M. S., Huang, X. andRothschild, L. P., Regularity of CR mappings between algebraic hypersurfaces,Invent. Math. 125 (1996), 13–36.
[C]Chern, S. S., On the projective structure of a real hypersurface inC n+1,Math. Scand. 36 (1975), 581–600.
[CJ1]Chern, S. S. andJi, S., Projective geometry and Riemann's mapping problem,Math. Ann. 302 (1995), 581–600.
[CJ2]Chern, S. S. andJi, S., On the Riemann mapping theorem,Ann. of Math. 144 (1996), 421–439.
[CM]Chern, S. S. andMoser, J. K., Real hypersurfaces in complex manifolds,Acta Math. 133 (1974), 219–271.
[E]Ebenfelt, P., On the unique continuation problem for CR mappings into nonminimal hypersurfaces,J. Geom. Anal. 6 (1996), 385–405.
[F]Faran, J., Segre families and real hypersurfaces,Invent. Math. 60 (1980), 135–172.
[H]Huang, X., On some problems in several complex variables and CR geometry, inProceedings of ICCM (Yau, S. T., ed.), pp. 231–244, International Press, Cambridge, Mass., 2000.
[HJ]Huang, X. andJi, S., Global holomorphic extension of a local map and a Riemann mapping theorem for algebraic domains,Math. Res. Lett. 5 (1998), 247–260.
[MW]Moser, J. andWebster, S. M., Normal forms for real surfaces inC 2 near complex tangents and hyperbolic surface transformations,Acta Math. 150 (1983), 255–296.
[W]Webster, S. M., On the mapping problem for algebraic real hypersurfaces,Invent. Math. 43 (1977), 53–68.
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Supported in part by NSF-9970439.
Supported in part by NSF and RGC at Hong Kong.
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Huang, X., Ji, S. & Yau, S.S.T. An example of a real analytic strongly pseudoconvex hypersurface which is not holomorphically equivalent to any algebraic hypersurface. Ark. Mat. 39, 75–93 (2001). https://doi.org/10.1007/BF02388792
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DOI: https://doi.org/10.1007/BF02388792