@article{AFST_2005_6_14_2_215_0, author = {Merker, Jo\"el}, title = {\'Etude de la r\'egularit\'e analytique de l'application de r\'eflexion {CR} formelle}, journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques}, pages = {215--330}, publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques}, address = {Toulouse}, volume = {6e s{\'e}rie, 14}, number = {2}, year = {2005}, mrnumber = {2141182}, zbl = {1090.32021}, language = {fr}, url = {http://www.numdam.org/item/AFST_2005_6_14_2_215_0/} }
TY - JOUR AU - Merker, Joël TI - Étude de la régularité analytique de l'application de réflexion CR formelle JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2005 SP - 215 EP - 330 VL - 14 IS - 2 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/item/AFST_2005_6_14_2_215_0/ LA - fr ID - AFST_2005_6_14_2_215_0 ER -
%0 Journal Article %A Merker, Joël %T Étude de la régularité analytique de l'application de réflexion CR formelle %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2005 %P 215-330 %V 14 %N 2 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/item/AFST_2005_6_14_2_215_0/ %G fr %F AFST_2005_6_14_2_215_0
Merker, Joël. Étude de la régularité analytique de l'application de réflexion CR formelle. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 14 (2005) no. 2, pp. 215-330. http://www.numdam.org/item/AFST_2005_6_14_2_215_0/
[Ar1968] On the solutions of analytic equations, Invent. Math. 5, p. 277-291 (1968). | MR | Zbl
-[Ar1969] Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36, p. 23-58 (1969). | Numdam | MR | Zbl
-[BR1988] Germs of CR maps between real analytic hypersurfaces, Invent. Math. 93, no. 3, p. 481-500 (1988). | MR | Zbl
, -[BR1990] Geometric properties of mappings between hypersurfaces in complex space, J. Differential Geom. 31, p. 473-499 (1990). | MR | Zbl
, -[BR1995] Mappings of real algebraic hypersurfaces, J. Amer. Math. Soc. 8, p. 997-1015 (1995). | MR | Zbl
, -[BER1996] Algebraicity of holomorphic mappings between real algebraic sets in Cn, Acta Math. 177, no. 2, p. 225-273 (1996). | MR | Zbl
, , -[BER1997] Parametrization of local biholomorphisms of real analytic hypersurfaces, Asian J. Math. 1, no. 1, p. 1-16 (1997). | MR | Zbl
, , -[BER1998] CR automorphisms of real analytic manifolds in complex space, Comm. Anal. Geom. 6, p. 291-315 (1998). | MR | Zbl
, , -[BER1999a] Real submanifolds in complex space and their mappings. Princeton Mathematical Series, 47, Princeton University Press Princeton, NJ, xii+404 pp (1999). | MR | Zbl
, , -[BER1999b] Rational dependence of smooth and analytic CR mappings on their jets, Math. Ann. 315, p. 205-249 (1999). | MR | Zbl
, , -[BER2000] Convergence and finite determination of formal CR mappings, J. Amer. Math. Soc. 13, p. 697-723 (2000). | MR | Zbl
, , -[BER2003] Dynamics of the Segre varieties of a real submanifold in complex space, J. Algebraic Geom. 12, no. 1, p. 81-106 (2003). | MR | Zbl
, , -[BJT1985] On the analyticity of CR mappings, Ann. of Math. 122, no. 2, p. 365-400 (1985). | MR | Zbl
, , -[BMR2002] Reflection ideals and mappings between generic submanifolds in complex space, J. Geom. Anal. 12, no. 4, p. 543-580 (2002). Preprint électronique : arXiv/abs/math/0012243. | MR | Zbl
, , -[BRZ2001] Equivalences of real submanifolds in complex space, J. Differential Geom. 59, no. 2, p. 301-351 (2001). | MR | Zbl
, , -[CM1974] Real hypersurfaces in complex manifolds, Acta Math. 133, p. 219-271( 1974). | MR | Zbl
, -[CMS1999] Holomorphic maps of algebraic CR manifolds, Internat. Math. Res. Notices , no.1, p. 1-29 (1999). | MR | Zbl
, , -[CPS1999] Analyticité des applications CR, C. R. Acad. Sci. Paris Sér. I Math. 329, no. 6, p. 489-494 (1999). | MR | Zbl
, , -[CPS2000] On partial analyticity of CR mappings, Math. Z. 235, p. 541-557 (2000). | MR | Zbl
, , -[CDMS2002] Sur l'analyticité des applications CR lisses à valeurs dans un ensemble algébrique réel, C. R. Acad. Sci. Paris Sér. I 334, p. 953-956 (2002). | MR | Zbl
, , , -[Da2001] On the analyticity of smooth CR mappings between real analytic CR manifolds, Michigan Math. J. 49, no. 3, p. 583-603 (2001). | MR | Zbl
-[DM2002] Sur la convergence d'applications formelles entre sous-variétés analytiques réelles, Bull. Sci. Math. 126, p. 831-854 (2002). | MR | Zbl
, -[De1985] Le principe de réflexion en des points de faible pseudoconvexité pour des applications holomorphes propres , Invent. Math. 79, no. 1, p. 197-215 (1985). | MR | Zbl
-[De1986] Sur le prolongement d'applications holomorphes , Séminaire sur les équations aux dérivées partielles , 1985-1986, Exp. No. XVI, 10 pp., École Polytech, Palaiseau, 1986. | Numdam | MR | Zbl
-[DF1978] Pseudoconvex domains with real analytic boundary, Ann. of Math. 107, no. 2, p. 371-384 (1978). | MR | Zbl
, -[DF1988] Proper holomorphic mappings between real-analytic pseudoconvex domains in Cn, Math. Ann. 282, no. 4, p. 681-700 (1988). | MR | Zbl
, -[DW1980] A reflection principle for degenerate real hypersurfaces, Duke Math. J. 47, no. 4, p. 835-843 (1980). | MR | Zbl
, -[DFY1994] Biholomorphisms in dimension 2, J. Geom. Anal. 4, no. 4, p. 539-552 (1994). | MR | Zbl
, , -[DP1995] Proper holomorphic maps in dimension 2 extend, Indiana Univ. Math. J. 44, no. 4, p. 1089-1126 (1995 ). | MR | Zbl
, -[DP1998] Reflection principle in higher dimensions, Proceedings of the International Congress of Mathematicians, Vol II (Berlin 1998), Doc. Math. 1998, Extra Vol. II, p. 703-712. | MR | Zbl
, -[DP2003] Regularity of continuous CR-maps in arbitrary dimension, Michigan Math. J. 51, p. 111-140 (2003). | MR | Zbl
, -[Eb1998] Normal forms and biholomorphic equivalence of real hypersurfaces in C3, Indiana Univ. Math. J. 47, no. 2, p. 311-366 (1998). | MR | Zbl
-[Eb2002] On the analyticity of CR mappings between nonminimal hypersurfaces, Math. Ann. 322, no. 3, p. 583-602 (2002). | MR | Zbl
-[Fo1991] Extending proper holomorphic mappings of positive codimension, Invent. Math. 95, no. 1, p. 31-62 (1989). | MR | Zbl
-[GM2003] Symmetries of partial differential equations, J. Korean Math. Soc. 40, no. 3, p. 517-561 (2003). | MR | Zbl
, -[GM2004] Nonalgebraizable real analytic tubes in Cn, Math. Z. 247, no. 2, p. 337-383 (2004). | MR | Zbl
, -[Go1996] Divergence of the normalization for real Lagrangian surfaces near complex tangents, Pacific Math. J. 176, p. 311-324 (1996). | MR | Zbl
-[Ha1983] Analyticity of CR equivalences between some real analytic hypersurfaces in Cn with degenerate Levi-forms , Invent. Math 73, no. 1, p. 51-69 (1983). | MR | Zbl
-[Ha1990] Rigidity of CR submanifolds and analyticity of CR immersions , Math. Ann. 287, no. 2, p. 229-238 (1990). | MR | Zbl
-[Hi1973] Introduction to real-analytic sets and real-analytic maps, Quaderni dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche, Istituto Matematico "L. Tonelli" dell'Università di Pisa, 1973, iii+162 pp. | MR
-[HK1995] On a problem of Moser , Duke Math. J. 78, no. 1, p. 213-228 (1995). | MR | Zbl
, -[La2000] Holomorphic maps of real submanifolds in complex spaces of different dimensions, Pacific Math. J. 201, no. 2, p. 357-387 (2001). | MR | Zbl
-[Le1977] On the boundary behaviour of holomorphic mappings, Contrib. Centro Linceo Inter. Sc. Mat. e Loro Appl. No. 35, Accad. Naz. Lincei (1977), 1-8
-; reprint in the 2 vols, Contemporary mathematicians, Birkhäuser , Boston (2002).
,[Ma1967] Ideals of Differentiable Functions, Tata Institute of Fundamental Research Studies in Mathematics, No. 3, Tata Institute of Fundamental Research, Bombay; Oxford University Press , London (1967), vii+106 pp. | MR | Zbl
-[Me1994] Global minimality of generic manifolds and holomorphic extendibility of CR functions, Internat. Math. Res. Notices, no. 8, p. 329-342 (1994). | MR | Zbl
-[Me1997a] On removable singularities for CR functions in higher codimension, Internat. Math. Res. Notices, no. 1, p. 21-56 (1997). | MR | Zbl
-[Me1997b] On the Schwarz symmetry principle in three-dimensional complex euclidean space, Prépublication de l'École Normale Supérieure, 25, 62 pp (1997).
-[Me1998] Vector field construction of Segre sets , Preprint 1998, augmented in 2000; downloadable at arXiv.org/abs/math.CV/9901010.
-[Me1999] On the convergence of S-nondegenerate formal CR maps between real analytic CR manifolds, Preprint, 1999 ; downloadable at: arXiv.org/abs/math.CV/9901027.
-[Me2000] Étude de la régularité analytique de l'application de symétrie CR formelle, Preprint, June 2000 ; downloadable at: arXiv.org/math/abs/0005290.
-[Me2001a] On the partial algebraicity of holomorphic mappings between two real algebraic sets in the complex euclidean spaces of different dimensions, Bull. Soc. Math. France 129, no. 4, p. 547-591 (2001). | Numdam | MR | Zbl
-[Me2001b] Convergence of formal invertible CR mappings between minimal holomorphically nondegenerate real analytic hypersurfaces , Int. J. Math. Sci., 26, no. 5, p. 281-302 (2001). | MR | Zbl
-[Me2001c] Étude de la régularité analytique de l'application de symétrie CR formelle, C. R. Acad. Sci. Paris Sér. I Math. 333, no. 3, p. 165-168 (2001). | MR | Zbl
-[Me2001d] Note on double reflection and algebraicity of holomorphic mappings, Annales de la Faculté des Sciences de Toulouse 9, no. 5, p. 689-721 (2001). | Numdam | MR | Zbl
-[Me2002] On envelopes of holomorphy of domains covered by Levi-flat hats and the reflection principle, Ann. Inst. Fourier Grenoble 52, no. 5, p. 1443-1523 (2002). | Numdam | MR | Zbl
-[Me2003] On the local geometry of generic submanifolds of Cn and the analytic reflection principle (Part I, Viniti, Kluwer, to appear, 80 pp.
-[Me2004] Systèmes complètement intégrables d'équations aux dérivées partielles analytiques : géométrie locale des sous-variétés des solutions , en préparation.
-[MM1999] On the Schwarz symmetry principle in a model case, Proc. Amer. Math. Soc. 127, no. 4, p. 1097-1102 (1999 ). | MR | Zbl
, -[MMZ2002] Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CRmanifolds , Asian J. Math. 7, no. 4, p. 493-509 (2003). | MR | Zbl
, , -[MMZ2003] Approximation and convergence of formal CR-mappings, Int. Math. Res. Not. , no. 4, p. 211-242 (2003). | MR | Zbl
, , -[Mi1998] Germs of holomorphic mappings between real algebraic hypersurfaces, Ann. Inst. Fourier Grenoble 48, no. 3, p. 1025-1043 (1998). | Numdam | MR | Zbl
-[Mi2002] On the convergence of formal mappings , Comm. Anal. Geom. 10, no. 1, p. 23-59 (2002). | MR | Zbl
-[Mi2000] Formal biholomorphic maps of real analytic hypersurfaces, Math. Research Lett. 7, no. 2-3, p. 343-359 (2000). | MR | Zbl
-[MW1983] Normal forms for real surfaces in C2 near complex tangents and hyperbolic surface transformations, Acta Math. 150, no. 3-4, p. 255-296 (1983). | MR | Zbl
, -[Na1966] Linear differential systems with singularities and applications to transitive Lie algebras, J. Math. Soc. Japan 18, p. 398-404 (1966). | MR | Zbl
-[Ne1997] On solutions of real analytic equations , Proc. Amer. Math. Soc. 125, no. 3, p. 2531-2535 (1997). | MR | Zbl
-[Pi1975] On the analytic continuation of holomorphic mappings (Russian, Mat. Sb. (N.S.) 98(140) no. 3 (11), p. 375-392, p. 416-435, p. 495-496 (1975). | MR | Zbl
-[Pi1978] Holomorphic mappings of real-analytic hypersurfaces (Russian, Mat. Sb. (N.S.) 105(147), no. 4, p. 574-593, 640 (1978 ). | MR
-[PV2001] Analytic sets and the boundary regularity of CR mappings, Proc. Amer. Math. Soc. 129, no. 9, p. 2623-2632 (2001 ). | MR | Zbl
, -[Pu1990] Holomorphicity of CR-mappings into a space of large dimension, Mat. Zametki 48, no. 3, p. 147-149 (1990). | MR | Zbl
-[Sch1870] Ueber einige Abbildungsaufgaben, Journal für reine und angewandte Mathematik, p. 105-120 (1870).
-[Se1931a] Questioni geometriche legate colla teoria delle funzioni di due variabili complesse, Bollettino della unione matematica italiana, 10, p. 269-274 (1931). | JFM
-[Se1931b] Intorno al problema di Poincaré della rappresentazione pseudoconforme, Rend. Acc. Lincei, VI, Ser. 13, 676-683 (1931). | JFM | Zbl
-[Se1932] Questioni geometriche legate colla teoria delle funzioni di due variabili complesse, Rend. Sem. Mat. Roma, II (memorie), Ser. 7, no. 2, p. 59-107 (1932). | Zbl
-[Sh2000] Analytic continuation of germs of holomorphic mappings between real hypersurfaces in Cn, Michigan Math. J. 47, no. 1, p. 133-149 (2000). | MR | Zbl
-[Sh2003] Analytic continuation of holomorphic correspondences and equivalence of domains in Cn, Invent. Math. 152, no. 3, p. 665-682 (2003). | MR | Zbl
-[SS1996] On CR mappings between algebraic Cauchy-Riemann manifolds and separate algebraicity for holomorphic functions , Trans. Amer. Math. Soc. 348, no. 2, p. 767-780 (1996). | MR | Zbl
, -[St1995] Infinitesimal CR automorphisms of rigid hypersurfaces of the space of n complex variables, Amer. J. Math. 117, no. 1, p. 141-167 (1995). | MR | Zbl
-[St1996] Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118, no. 1, p. 209-233 (1996). | MR | Zbl
-[Su1973] Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180, p. 171-188 (1973). | MR | Zbl
-[Te1996] Communication orale.
-[Tr1986] Sur le prolongement holomorphe des fonctions CR définies sur une hypersurface réelle de classe C2 dans Cn , Invent. Math. 83, p. 583-592 (1986). | MR | Zbl
-[Tr1990] Sur la propagation des singularités dans les variétés CR, Bull. Soc. Math. Fr. 118, no. 4, p. 403-450 (1990). | Numdam | MR | Zbl
-[Tr2000] Recension du livre [BER1999b], Gazette des mathématiciens 85, p. 82-84 (2000).
-[Tu1988] Extending CR functions on a manifold of finite type over a wedge (Russian, Mat. Sb. (N.S.) 136(178) (1988), no. 1, 128-139. English transl. in Math. USSR-Sb. 64, no. 1, p. 129-140 (1989). | MR | Zbl
-[Tu1994] Connections and propagation of analyticity for CR functions, Duke Math. J. 73, no. 1, p. 1-24 (1994). | MR | Zbl
-[VdW1970] Algebra, Vol 1 and 2. Translated by Fred Blum and John R. Schulenberger Frederick Ungar Publishing Co., New York 1970 xiv+265 pp. | MR
-[We1977] On the mapping problem for algebraic real hypersurfaces, Invent. Math. 43, no. 1, p. 53-68 (1977). | MR | Zbl
-[We1978] On the reflection principle in several complex variables, Proc. Amer. Math. Soc. 71, no. 1, p. 26-28 (1978). | MR | Zbl
-[We1982] Holomorphic mappings of domains with generic corners, Proc. Amer. Math. Soc. 86, no. 2, p. 236-240 (1982). | MR | Zbl
-[We1992] Holomorphic symplectic normalization of a real function, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4 )19, no. 1, p. 69-86 (1992). | Numdam | MR | Zbl
-[Za1997] Germs of local automorphisms of real-analytic CR structures and analytic dependence on k-jets, Math. Research Lett. 4, no. 6, p. 823-842 (1997). | MR | Zbl
-[ZS1960] Commutative algebra, 2 vols, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J., Toronto-London- New York, 1958, 1960. | MR
, -