Regularity of CR maps between convex hypersurfaces of finite type
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- by Bernard Coupet, Hervé Gaussier and Alexandre Sukhov
- Proc. Amer. Math. Soc. 127 (1999), 3191-3200
- DOI: https://doi.org/10.1090/S0002-9939-99-04908-4
- Published electronically: April 27, 1999
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Abstract:
We study rigidity and regularity properties of CR maps between smooth convex hypersurfaces of finite type in $\mathbb C^{n+1}.$References
- Eric Bedford and Sergey Pinchuk, Domains in $\textbf {C}^{n+1}$ with noncompact automorphism group, J. Geom. Anal. 1 (1991), no. 3, 165–191. MR 1120679, DOI 10.1007/BF02921302
- E. Bedford and S. I. Pinchuk, Convex domains with noncompact groups of automorphisms, Mat. Sb. 185 (1994), no. 5, 3–26 (Russian, with Russian summary); English transl., Russian Acad. Sci. Sb. Math. 82 (1995), no. 1, 1–20. MR 1275970, DOI 10.1070/SM1995v082n01ABEH003550
- S. Bell, Local regularity of CR homeomorphisms, Duke Math. J. 57 (1988), no. 1, 295–300. MR 952236, DOI 10.1215/S0012-7094-88-05713-4
- S. Bell and D. Catlin, Regularity of CR mappings, Math. Z. 199 (1988), no. 3, 357–368. MR 961816, DOI 10.1007/BF01159784
- David Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. (2) 120 (1984), no. 3, 529–586. MR 769163, DOI 10.2307/1971087
- Bernard Coupet, Sergey Pinchuk, and Alexandre Sukhov, On boundary rigidity and regularity of holomorphic mappings, Internat. J. Math. 7 (1996), no. 5, 617–643. MR 1411304, DOI 10.1142/S0129167X96000335
- Bernard Coupet and Alexandre Sukhov, On CR mappings between pseudoconvex hypersurfaces of finite type in $\mathbf C^2$, Duke Math. J. 88 (1997), no. 2, 281–304. MR 1455521, DOI 10.1215/S0012-7094-97-08811-6
- Klas Diederich and Gregor Herbort, Pseudoconvex domains of semiregular type, Contributions to complex analysis and analytic geometry, Aspects Math., E26, Friedr. Vieweg, Braunschweig, 1994, pp. 127–161. MR 1319347
- John Erik Fornæss and Nessim Sibony, Construction of P.S.H. functions on weakly pseudoconvex domains, Duke Math. J. 58 (1989), no. 3, 633–655. MR 1016439, DOI 10.1215/S0012-7094-89-05830-4
- H.Gaussier, Characterization of convex domains with noncompact automorphism group, Mich. J. Math. 44-2 (1997), 375-388.
- Jeffery D. McNeal, Convex domains of finite type, J. Funct. Anal. 108 (1992), no. 2, 361–373. MR 1176680, DOI 10.1016/0022-1236(92)90029-I
- David Mumford, Algebraic geometry. I, Grundlehren der Mathematischen Wissenschaften, No. 221, Springer-Verlag, Berlin-New York, 1976. Complex projective varieties. MR 0453732
- L. Nirenberg, S. Webster, and P. Yang, Local boundary regularity of holomorphic mappings, Comm. Pure Appl. Math. 33 (1980), no. 3, 305–338. MR 562738, DOI 10.1002/cpa.3160330306
- S.Pinchuk, On the analytic continuation of holomorphic mappings, Math. USSR Sbornik 27 (1975), 375-392.
- S. I. Pinchuk and Sh. I. Tsyganov, Smoothness of CR-mappings between strictly pseudoconvex hypersurfaces, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 5, 1120–1129, 1136 (Russian); English transl., Math. USSR-Izv. 35 (1990), no. 2, 457–467. MR 1024457, DOI 10.1070/IM1990v035n02ABEH000714
- Nessim Sibony, Une classe de domaines pseudoconvexes, Duke Math. J. 55 (1987), no. 2, 299–319 (French). MR 894582, DOI 10.1215/S0012-7094-87-05516-5
- A.Sukhov, On boundary regularity of holomorphic mappings, Russian Acad. Sci. Sb. Math. 83-2 (1995), 541-551.
- S. M. Webster, On the mapping problem for algebraic real hypersurfaces, Invent. Math. 43 (1977), no. 1, 53–68. MR 463482, DOI 10.1007/BF01390203
Bibliographic Information
- Bernard Coupet
- Affiliation: CMI (Center of Mathematics & Information), University of Provence, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
- Hervé Gaussier
- Affiliation: CMI (Center of Mathematics & Information), University of Provence, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
- Alexandre Sukhov
- Affiliation: CMI (Center of Mathematics & Information), University of Provence, 39 rue Joliot-Curie, 13453 Marseille Cedex 13, France
- MR Author ID: 242836
- Received by editor(s): January 15, 1998
- Published electronically: April 27, 1999
- Communicated by: Steven R. Bell
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3191-3200
- MSC (1991): Primary 32H40, 32H99; Secondary 32F40, 32G07, 32H15, 32H35, 32M99
- DOI: https://doi.org/10.1090/S0002-9939-99-04908-4
- MathSciNet review: 1610940