Proper holomorphic mappings between real analytic domains in Cn
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Duke Mathematical Journal

Proper holomorphic mappings between real analytic domains in $\mathbf{C}_n$

Xiaojun Huang and Yifei Pan

Source: Duke Math. J. Volume 82, Number 2 (1996), 437-446.

First Page PDF: View first page of article (PDF, 107 KB)

Primary Subjects: 32H35
Secondary Subjects: 32H40

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077245040
Mathematical Reviews number (MathSciNet): MR1387236
Zentralblatt MATH identifier: 0853.32030
Digital Object Identifier: doi:10.1215/S0012-7094-96-08219-8

References

[Alx1] H. Alexander, Boundary behavior of certain holomorphic maps, Michigan Math. J. 38 (1991), no. 1, 117–128.
Mathematical Reviews (MathSciNet): MR92c:32031
Zentralblatt MATH: 0735.32005
Digital Object Identifier: doi:10.1307/mmj/1029004267
Project Euclid: euclid.mmj/1029004267
[Alx2] H. Alexander, On a generalized Hopf lemma, preprint.
[ABR] S. Alinhac, M. S. Baouendi, and L. P. Rothschild, Unique continuation and regularity at the boundary for holomorphic functions, Duke Math. J. 61 (1990), no. 2, 635–653.
Mathematical Reviews (MathSciNet): MR92d:32033
Zentralblatt MATH: 0718.32021
Digital Object Identifier: doi:10.1215/S0012-7094-90-06123-X
Project Euclid: euclid.dmj/1077296830
[BBR] M. S. Baouendi, S. Bell, and L. P. Rothschild, Mappings of three-dimensional CR manifolds and their holomorphic extension, Duke Math. J. 56 (1988), no. 3, 503–530.
Mathematical Reviews (MathSciNet): MR90a:32035
Zentralblatt MATH: 0655.32015
Digital Object Identifier: doi:10.1215/S0012-7094-88-05621-9
Project Euclid: euclid.dmj/1077306715
[BJT] M. S. Baouendi, H. Jacobowitz, and F. Treves, On the analyticity of CR mappings, Ann. of Math. (2) 122 (1985), no. 2, 365–400.
Mathematical Reviews (MathSciNet): MR87f:32044
Zentralblatt MATH: 0583.32021
Digital Object Identifier: doi:10.2307/1971307
JSTOR: links.jstor.org
[BR1] M. S. Baouendi and L. P. Rothschild, Germs of CR maps between real analytic hypersurfaces, Invent. Math. 93 (1988), no. 3, 481–500.
Mathematical Reviews (MathSciNet): MR90a:32036
Zentralblatt MATH: 0653.32020
Digital Object Identifier: doi:10.1007/BF01410197
[BR2] M. S. Baouendi and L. P. Rothschild, Geometric properties of mappings between hypersurfaces in complex space, J. Differential Geom. 31 (1990), no. 2, 473–499.
Mathematical Reviews (MathSciNet): MR91g:32032
Zentralblatt MATH: 0702.32014
[BR3] M. S. Baouendi and L. P. Rothschild, A generalized complex Hopf lemma and its applications to CR mappings, Invent. Math. 111 (1993), no. 2, 331–348.
Mathematical Reviews (MathSciNet): MR95c:32017
Zentralblatt MATH: 0781.32021
Digital Object Identifier: doi:10.1007/BF01231291
[BR4] M. S. Baouendi and L. P. Rothschild, Normal forms for generic manifolds and holomorphic extension of CR functions, J. Differential Geom. 25 (1987), no. 3, 431–467.
Mathematical Reviews (MathSciNet): MR88m:32039
Zentralblatt MATH: 0629.32016
[BR5] M. S. Baouendi and L. P. Rothschild, Unique continuation and a Schwarz reflection principle for analytic sets, Comm. Partial Differential Equations 18 (1993), no. 11, 1961–1970.
Mathematical Reviews (MathSciNet): MR94i:32014
Zentralblatt MATH: 0794.32015
[BR6] M. S. Baouendi and L. P. Rothschild, A local Hopf lemma and unique continuation for harmonic functions, Internat. Math. Res. Notices (1993), no. 8, 245–251.
Mathematical Reviews (MathSciNet): MR94i:31008
Zentralblatt MATH: 0787.31002
Digital Object Identifier: doi:10.1155/S1073792893000273
[BR7] M. S. Baouendi and L. P. Rothschild, Remarks on the generic rank of a CR mapping, J. Geom. Anal. 2 (1992), no. 1, 1–9.
Mathematical Reviews (MathSciNet): MR92m:32025
Zentralblatt MATH: 0748.32011
Digital Object Identifier: doi:10.1007/BF01895704
[BT] S. Baouendi and F. Treves, About the holomorphic extension of CR functions on real hypersurfaces in complex space, Duke Math. J. 51 (1984), no. 1, 77–107.
Mathematical Reviews (MathSciNet): MR85j:32021
Zentralblatt MATH: 0564.32011
Digital Object Identifier: doi:10.1215/S0012-7094-84-05105-6
Project Euclid: euclid.dmj/1077303669
[Be] E. Bedford, Proper holomorphic mappings from domains with real analytic boundary, Amer. J. Math. 106 (1984), no. 3, 745–760.
Mathematical Reviews (MathSciNet): MR86a:32053
Zentralblatt MATH: 0556.32013
[BB] E. Bedford and S. Bell, Proper self-maps of weakly pseudoconvex domains, Math. Ann. 261 (1982), no. 1, 47–49.
Mathematical Reviews (MathSciNet): MR84c:32026
Zentralblatt MATH: 0499.32016
Digital Object Identifier: doi:10.1007/BF01456408
[B] S. Bell, Analytic hypoellipticity of the $\bar \partial$-Neumann problem and extendability of holomorphic mappings, Acta Math. 147 (1981), no. 1-2, 109–116.
Mathematical Reviews (MathSciNet): MR83a:32011
Zentralblatt MATH: 0475.32010
Digital Object Identifier: doi:10.1007/BF02392871
[BC] S. Bell and D. Catlin, Regularity of CR mappings, Math. Z. 199 (1988), no. 3, 357–368.
Mathematical Reviews (MathSciNet): MR89i:32028
Zentralblatt MATH: 0639.32011
Digital Object Identifier: doi:10.1007/BF01159784
[BL] S. Bell and L. Lempert, A $C\sp \infty$ Schwarz reflection principle in one and several complex variables, J. Differential Geom. 32 (1990), no. 3, 899–915.
Mathematical Reviews (MathSciNet): MR91k:32017
Zentralblatt MATH: 0716.32002
[DF] K. Diederich and J. Fornæss, Proper holomorphic mappings between real-analytic pseudoconvex domains in ${\bf C}\sp n$, Math. Ann. 282 (1988), no. 4, 681–700.
Mathematical Reviews (MathSciNet): MR89m:32045
Zentralblatt MATH: 0661.32025
Digital Object Identifier: doi:10.1007/BF01462892
[DW] K. Diederich and S. Webster, A reflection principle for degenerate real hypersurfaces, Duke Math. J. 47 (1980), no. 4, 835–843.
Mathematical Reviews (MathSciNet): MR82j:32046
Zentralblatt MATH: 0451.32008
Digital Object Identifier: doi:10.1215/S0012-7094-80-04749-3
Project Euclid: euclid.dmj/1077314339
[Hir] H. Hironaka, Subanalytic sets, Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, pp. 453–493.
Mathematical Reviews (MathSciNet): MR51:13275
Zentralblatt MATH: 0297.32008
[HK] X. Huang and S. Krantz, A unique continuation problem for holomorphic mappings, Comm. Partial Differential Equations 18 (1993), no. 1-2, 241–263.
Mathematical Reviews (MathSciNet): MR94b:32022
Zentralblatt MATH: 0781.32018
[HKMP] X. Huang, S. Krantz, D. Ma, and Y. Pan, A Hopf lemma for holomorphic functions and applications, Complex Variables Theory Appl. 26 (1995), no. 4, 273–276.
Mathematical Reviews (MathSciNet): MR96d:30027
Zentralblatt MATH: 0837.30019
[Le] H. Lewy, On the boundary behavior of holomorphic mappings, Atti. Accad. Naz. Rend. Lincei Cl. Sci. Mat. Natur. Appl. Mat. 35 (1977), 1–8.
[Pan1] Y. Pan, Proper holomorphic self-mappings of Reinhardt domains, Math. Z. 208 (1991), no. 2, 289–295.
Mathematical Reviews (MathSciNet): MR93f:32029
Zentralblatt MATH: 0727.32011
[Pan2] Y. Pan, Real analyticity of homeomorphic CR mappings between real analytic hypersurfaces in ${\bf C}\sp 2$, Proc. Amer. Math. Soc. 123 (1995), no. 2, 373–380.
Mathematical Reviews (MathSciNet): MR95c:32027
Zentralblatt MATH: 0813.32017
Digital Object Identifier: doi:10.2307/2160891
[Pi] S. I. Pinčuk, Proper holomorphic maps of strictly pseudoconvex domains, Sibirsk. Mat. Ž. 15 (1974), 909–917, 959.
Mathematical Reviews (MathSciNet): MR50:7586
Zentralblatt MATH: 0289.32011
[R] W. Rudin, Function theory in the unit ball of ${\bf C}\sp{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York, 1980.
Mathematical Reviews (MathSciNet): MR82i:32002
Zentralblatt MATH: 0495.32001
[S] M. H. Schwartz, Lectures on stratification of complex analytic sets, Tata Institute of Fundamental Research Lectures on Mathematics, No. 38, Tata Institute of Fundamental Research, Bombay, 1966.
Mathematical Reviews (MathSciNet): MR35:5660
Zentralblatt MATH: 0169.41404
[Tu] A. E. Tumanov, Extension of CR-functions into a wedge from a manifold of finite type, Mat. Sb. (N.S.) 136(178) (1988), no. 1, 128–139.
Mathematical Reviews (MathSciNet): MR89m:32027
Zentralblatt MATH: 0692.58005
[W] S. Webster, On the mapping problem for algebraic real hypersurfaces, Invent. Math. 43 (1977), no. 1, 53–68.
Mathematical Reviews (MathSciNet): MR57:3431
Zentralblatt MATH: 0348.32005
Digital Object Identifier: doi:10.1007/BF01390203

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