Geodesic
Convergence and finite determination of formal CR mappings
Baouendi, M.1 ; Ebenfelt, P.2 ; Rothschild, Linda1
1 Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112
2 Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Journal of the American Mathematical Society, Tome 13 (2000) no. 4, pp. 697-723

Voir la notice de l'article provenant de la source American Mathematical Society

It is shown that a formal mapping between two real-analytic hypersurfaces in complex space is convergent provided that neither hypersurface contains a nontrivial holomorphic variety. For higher codimensional generic submanifolds, convergence is proved e.g. under the assumption that the source is of finite type, the target does not contain a nontrivial holomorphic variety, and the mapping is finite. Finite determination (by jets of a predetermined order) of formal mappings between smooth generic submanifolds is also established.
DOI : 10.1090/S0894-0347-00-00343-X

Baouendi, M. 1 ; Ebenfelt, P. 2 ; Rothschild, Linda 1

1 Department of Mathematics, 0112, University of California at San Diego, La Jolla, California 92093-0112
2 Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden 
@article{10_1090_S0894_0347_00_00343_X,
     author = {Baouendi, M. and Ebenfelt, P. and Rothschild, Linda},
     title = {Convergence and finite determination of formal {CR} mappings},
     journal = {Journal of the American Mathematical Society},
     pages = {697--723},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2000},
     doi = {10.1090/S0894-0347-00-00343-X},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00343-X/}
}
TY  - JOUR
AU  - Baouendi, M.
AU  - Ebenfelt, P.
AU  - Rothschild, Linda
TI  - Convergence and finite determination of formal CR mappings
JO  - Journal of the American Mathematical Society
PY  - 2000
SP  - 697
EP  - 723
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00343-X/
DO  - 10.1090/S0894-0347-00-00343-X
ID  - 10_1090_S0894_0347_00_00343_X
ER  - 
%0 Journal Article
%A Baouendi, M.
%A Ebenfelt, P.
%A Rothschild, Linda
%T Convergence and finite determination of formal CR mappings
%J Journal of the American Mathematical Society
%D 2000
%P 697-723
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-00-00343-X/
%R 10.1090/S0894-0347-00-00343-X
%F 10_1090_S0894_0347_00_00343_X
Baouendi, M.; Ebenfelt, P.; Rothschild, Linda. Convergence and finite determination of formal CR mappings. Journal of the American Mathematical Society, Tome 13 (2000) no. 4, pp. 697-723. doi: 10.1090/S0894-0347-00-00343-X

[1] Artin, M. On the solutions of analytic equations Invent. Math. 1968 277 291

[2] Atiyah, M. F., Macdonald, I. G. Introduction to commutative algebra 1969

[3] Baouendi, M. S., Ebenfelt, P., Rothschild, L. P. Algebraicity of holomorphic mappings between real algebraic sets in 𝐶ⁿ Acta Math. 1996 225 273

[4] Baouendi, M. S., Ebenfelt, P., Rothschild, Linda Preiss CR automorphisms of real analytic manifolds in complex space Comm. Anal. Geom. 1998 291 315

[5] Baouendi, M. S., Ebenfelt, P., Rothschild, Linda Preiss Parametrization of local biholomorphisms of real analytic hypersurfaces Asian J. Math. 1997 1 16

[6] Baouendi, M. Salah, Ebenfelt, Peter, Rothschild, Linda Preiss Real submanifolds in complex space and their mappings 1999

[7] Baouendi, M. S., Rothschild, Linda Preiss Geometric properties of mappings between hypersurfaces in complex space J. Differential Geom. 1990 473 499

[8] Beloshapka, V. K. A uniqueness theorem for automorphisms of a nondegenerate surface in a complex space Mat. Zametki 1990

[9] Brieskorn, Egbert, Knã¶Rrer, Horst Plane algebraic curves 1986

[10] D’Angelo, John P. Several complex variables and the geometry of real hypersurfaces 1993

[11] Chern, S. S., Moser, J. K. Real hypersurfaces in complex manifolds Acta Math. 1974 219 271

[12] Gong, Xiang Hong Divergence for the normalization of real analytic glancing hypersurfaces Comm. Partial Differential Equations 1994 643 654

[13] Gong, Xianghong Divergence of the normalization for real Lagrangian surfaces near complex tangents Pacific J. Math. 1996 311 324

[14] Trjitzinsky, W. J. General theory of singular integral equations with real kernels Trans. Amer. Math. Soc. 1939 202 279

[15] Algebraic geometry, Arcata 1974 1979

[16] Huang, Xiaojun Schwarz reflection principle in complex spaces of dimension two Comm. Partial Differential Equations 1996 1781 1828

[17] Melrose, R. B. Equivalence of glancing hypersurfaces Invent. Math. 1976 165 191

[18] Milman, Pierre D. Complex analytic and formal solutions of real analytic equations in 𝐶ⁿ Math. Ann. 1978 1 7

[19] Moser, Jã¼Rgen K., Webster, Sidney M. Normal forms for real surfaces in 𝐶² near complex tangents and hyperbolic surface transformations Acta Math. 1983 255 296

[20] ŌShima, Toshio On analytic equivalence of glancing hypersurfaces Sci. Papers College Gen. Ed. Univ. Tokyo 1978 51 57

[21] Tanaka, Noboru On the pseudo-conformal geometry of hypersurfaces of the space of 𝑛 complex variables J. Math. Soc. Japan 1962 397 429

[22] Tumanov, A. E., Khenkin, G. M. Local characterization of holomorphic automorphisms of Siegel domains Funktsional. Anal. i Prilozhen. 1983 49 61

[23] Ward, Morgan Ring homomorphisms which are also lattice homomorphisms Amer. J. Math. 1939 783 787

[24] Webster, S. M. Holomorphic symplectic normalization of a real function Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 1992 69 86

[25] Zaitsev, Dmitri Germs of local automorphisms of real-analytic CR structures and analytic dependence on 𝑘-jets Math. Res. Lett. 1997 823 842

[26] Maclane, Saunders, Schilling, O. F. G. Infinite number fields with Noether ideal theories Amer. J. Math. 1939 771 782

Cité par Sources :