Mersenne banner

Livres, Actes et Séminaires du Centre Mersenne

  • Livres
  • Séminaires
  • Congrès
  • Tout
  • Auteur
  • Titre
  • Bibliographie
  • Plein texte
NOT
Entre et
  • Tout
  • Auteur
  • Titre
  • Date
  • Bibliographie
  • Mots-clés
  • Plein texte
  • Précédent
  • Journées équations aux dérivées partielles
  • Année 2003
  • article no. 12
  • Suivant
On some rigidity properties of mappings between CR-submanifolds in complex space
Francine Meylan ; Nordine Mir ; Dimitri Zaitsev
Journées équations aux dérivées partielles (2003), article no. 12, 20 p.
  • Résumé

We survey some recent results on holomorphic or formal mappings sending real submanifolds in complex space into each other. More specifically, the approximation and convergence properties of formal CR-mappings between real-analytic CR-submanifolds will be discussed, as well as the corresponding questions in the category of real-algebraic CR-submanifolds.

  • Détail
  • Export
  • Comment citer
MR   Zbl
DOI : 10.5802/jedp.626
  • BibTeX
  • RIS
  • EndNote
@incollection{JEDP_2003____A12_0,
     author = {Francine Meylan and Nordine Mir and Dimitri Zaitsev},
     title = {On some rigidity properties of mappings between {CR-submanifolds} in complex space},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {12},
     pages = {1--20},
     publisher = {Universit\'e de Nantes},
     year = {2003},
     doi = {10.5802/jedp.626},
     zbl = {02079447},
     mrnumber = {2050598},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.626/}
}
TY  - JOUR
AU  - Francine Meylan
AU  - Nordine Mir
AU  - Dimitri Zaitsev
TI  - On some rigidity properties of mappings between CR-submanifolds in complex space
JO  - Journées équations aux dérivées partielles
PY  - 2003
SP  - 1
EP  - 20
PB  - Université de Nantes
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.626/
DO  - 10.5802/jedp.626
LA  - en
ID  - JEDP_2003____A12_0
ER  - 
%0 Journal Article
%A Francine Meylan
%A Nordine Mir
%A Dimitri Zaitsev
%T On some rigidity properties of mappings between CR-submanifolds in complex space
%J Journées équations aux dérivées partielles
%D 2003
%P 1-20
%I Université de Nantes
%U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.626/
%R 10.5802/jedp.626
%G en
%F JEDP_2003____A12_0
Francine Meylan; Nordine Mir; Dimitri Zaitsev. On some rigidity properties of mappings between CR-submanifolds in complex space. Journées équations aux dérivées partielles (2003), article  no. 12, 20 p. doi : 10.5802/jedp.626. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.626/
  • Bibliographie
  • Cité par

[A68] Artin, M. - On the solutions of analytic equations. Invent. math. 5 (1968), 277-291. | MR | Zbl

[A69] Artin, M. - Algebraic approximation of structures over complete local rings. Inst. Hautes Etudes Sci. Publ. Math. 36, (1969), 23-58. | Numdam | MR | Zbl

[BER96] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - Algebraicity of holomorphic mappings between real algebraic sets in C n . Acta Math. 177 (1996), 225-273. | MR | Zbl

[BER97] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - Parametrization of local biholomorphisms of real analytic hypersurfaces. Asian J. Math. 1 (1997), 1-16. | MR | Zbl

[BER98] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - CR automorphisms of real analytic manifolds in complex space. Comm. Anal. Geom., 6, (1998), 291-315. | MR | Zbl

[BER99a] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - Real Submanifolds in Complex Space and Their Mappings. Princeton Math. Series 47, Princeton Univ. Press, 1999. | MR | Zbl

[BER99b] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - Rational dependence of smooth and analytic CR mappings on their jets. Math. Ann. 315 (1999), 205-249. | MR | Zbl

[BER00a] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - Convergence and finite determination of formal CR mappings. J. Amer. Math. Soc. 13 (2000), 697-723. | MR | Zbl

[BER00b] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - Local geometric properties of real submanifolds in complex space, Bull. Amer. Math. Soc., 37, (2000) 309-336. | MR | Zbl

[BER03] Baouendi, M.S.; Ebenfelt, P.; Rothschild, L.P. - Dynamics of the Segre varieties of a real submanifold in complex space, J. Algebraic Geom., 12 (2003), 81-106. | MR | Zbl

[BMR02] Baouendi, M.S.; Mir, N.; Rothschild, L.P. - Reflection ideals and mappings between generic submanifolds in complex space, J. Geom. Anal., 12, no. 4, (2002), 543-580. | MR | Zbl

[BRZ01a] Baouendi, M.S.; Rothschild, L.P.; Zaitsev, D. - Equivalences of real submanifolds in complex space. J. Differential Geom. 59 (2001), 301-351. | MR | Zbl

[BRZ01b] Baouendi, M.S.; Rothschild, L.P.; Zaitsev, D. - Points in general position in real-analytic submanifolds in C N and applications. Ohio State Univ. Math. Res. Inst. Publ., 9, (2001), 1-20. | MR | Zbl

[BN90] Bell, S.R.; Narasimhan, R. - Proper holomorphic mappings of complex spaces, Several Complex Variables (Heidelberg) (Barth, W., Narasimhan, R., Eds.), EMS, 69, Springer-Verlag, 1990. | MR | Zbl

[BG77] Bloom, T.; Graham, I. - On type conditions for generic real submanifolds of C n . Invent. math. 40 (1977), 217-243. | MR | Zbl

[C32a] Cartan, E. - Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes, Part I, Ann. Math. Pura Appl. 11, (1932), 17-90. | JFM

[C32b] Cartan, E. - Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes, Part II, Ann. Sc. Norm. Sup. Pisa 1, (1932), 333-354. | JFM | Numdam

[CM74] Chern, S.S.; Moser, J.K. - Real hypersurfaces in complex manifolds. Acta Math. 133 (1974), 219-271. | MR | Zbl

[CMS99] Coupet, B.; Meylan, F.; Sukhov, A. - Holomorphic maps of algebraic CR manifolds. Internat. Math. Res. Notices 1 (1999), 1-29. | MR | Zbl

[D'A82] D'Angelo, J.P. - Real hypersurfaces, orders of contact, and applications. Ann. of Math. (2) 115 (1982), no. 3, 615-637. | MR | Zbl

[D'A91] D'Angelo, J.P. - Finite type and the intersection of real and complex subvarieties. Several complex variables and complex geometry, Part 3(Santa Cruz, CA, 1989), 103-117, Proc. Sympos. Pure Math. 52, Part 3, Amer. Math. Soc., Providence, RI, 1991. | MR | Zbl

[Fo93] Forstnerič, F. - Proper holomorphic mappings: a survey. Several complex variables (Stockholm, 1987/1988), 297-363, Math. Notes 38, Princeton Univ. Press, Princeton, NJ, 1993. | MR | Zbl

[G02] Gong, X. - Existence of real-analytic surfaces with hyperbolic complex tangent that are formally but not holomorphically equivalent to quadrics, Indiana Univ. Math. J., (to appear). | MR | Zbl

[Hu94] Huang, X. - On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions. Ann. Inst. Fourier, (Grenoble) 44, no. 2, 433-463 (1994). | Numdam | MR | Zbl

[Hu01] Huang, X. - On some problems in several complex variables and CR geometry. First International Congress of Chinese Mathematicians (Beijing, 1998), 383-396, AMS/IP Stud. Adv. Math. 20, Amer. Math. Soc., Providence, RI, 2001. | MR | Zbl

[KZ01] Kim, S.-Y.; Zaitsev, D. - The equivalence and embeddings problems for CR structures of any codimension (preprint 2001).

[K72] Kohn, J.J. - Boundary behavior of ˉ∂ on weakly pseudo-convex manifolds of dimension two. J. Differential Geom. 6, (1972), 523-542. | MR | Zbl

[La01] Lamel, B. - Holomorphic maps of real submanifolds in complex spaces of different dimensions. Pacific J. Math. 201 (2001), no. 2, 357-387. | MR | Zbl

[Le86] Lempert, L. - On the boundary behavior of holomorphic mappings. Contributions to several complex variables, 193-215, Aspects Math., E9, Viehweg, Braunschweig, 1986. | MR | Zbl

[MMZ03] Meylan, F.; Mir, N.; Zaitsev, D. - Approximation and convergence of formal CR-mappings. Internat. Math. Res. Notices 4, (2003), 211-242. | MR | Zbl

[M98] Mir, N. - Germs of holomorphic mappings between real-algebraic hypersurfaces, Ann. Inst. Fourier, (Grenoble) 48 no. 4, (1998), 1025-1043. | Numdam | MR | Zbl

[M00] Mir, N.. - Formal biholomorphic maps of real analytic hypersurfaces. Math. Res. Lett. 7 (2000), 343-359. | MR | Zbl

[M02a] Mir, N.. - On the convergence of formal mappings. Comm. Anal. Geom. 10, no. 1, (2002), 23-59. | MR | Zbl

[M02b] Mir, N.. - Convergence of formal embeddings between real-analytic hypersurfaces in codimension one, J. Differential Geom. 62 (2002), 163-173. | MR | Zbl

[MW83] Moser, J.K.; Webster, S.M. - Normal forms for real surfaces in C 2 near complex tangents and hyperbolic surface transformations. Acta Math. 150 (1983), no. 3-4, 255-296. | MR | Zbl

[N62] Nagano, T. - Linear differential systems with singularities and an application to transitive Lie algebras. J. Math. Soc. Japan 14, (1962), 397-429. | MR

[Po07] Poincaré, H. - Les fonctions analytiques de deux variables et la représentation conforme, Rend. Circ. Mat. Palermo 23, (1907), 185-220. | JFM

[Pu90a] Pushnikov, A.Yu. - Holomorphicity of CR-mappings into a space of large dimension. Mat. Zametki 48 (1990), no. 3, 147-149. | MR | Zbl

[Pu90b] Pushnikov, A.Yu. - On the holomorphy of CR-mappings of real analytic hypersurfaces. Complex analysis and differential equations, 76-84, Bashkir. Gos. Univ., Ufa, 1990. | MR

[R03] Rothschild, L.P. - Mappings of real submanifolds in complex space, Contemp. Math., Amer. Math. Soc. (to appear). | MR

[S96] Stanton, N. - Infinitesimal CR automorphisms of real hypersurfaces, Amer. J. Math. 118, (1996), 209-233. | MR | Zbl

[Ta62] Tanaka, N. - On the pseudo-conformal geometry of hypersurfaces of the space of n complex variables J. Math. Soc. Japan, 14, 397-429, (1962). | MR | Zbl

[Tr00] Treves, F. - A treasure trove of geometry and analysis: the hyperquadric, Notices Amer. Math. Soc. 47, no. 10, (2000), 1246 -1256. | MR | Zbl

[V85] Vitushkin, A.G. - Holomorphic mappings and the geometry of hypersurfaces, Encyclopedia of Mathematical Sciences, Vol. 7, Several Complex Variables I, Springer-Verlag, Berlin, 1985, pp. 159-214. | MR | Zbl

[W77] Webster, S. - On the mapping problem for algebraic real hypersurfaces. Invent. math., 43, (1977), 53-68. | MR | Zbl

[Z97] Zaitsev, D. - Germs of local automorphisms of real analytic CR structures and analytic dependence on k-jets. Math. Res. Lett. 4 (1997), 823-842. | MR | Zbl

[Z99] Zaitsev, D. - Algebraicity of local holomorphisms between real-algebraic submanifolds in complex space, Acta Math., 183, (1999), 273-305. | MR | Zbl

[Z02] Zaitsev, D. - Unique jet determination of local CR-maps by their jets: a survey, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 13, (2002), 295-305. | MR | Zbl

Cité par Sources :

Diffusé par : Publié par : Développé par :
  • Nous suivre