We give a geometric approach to the proof of the -lemma. In particular, we point out the role pseudoconvexity plays in the proof.
Nous donnons une approche géométrique de la preuve de la -lemma. Nous soulignons, en particulier, le rôle que la pseudoconvexité joue dans la preuve.
Accepted:
Published online:
DOI: 10.5802/afst.1485
Eric Bedford 1; Tanya Firsova 2
@article{AFST_2016_6_25_1_1_0,
author = {Eric Bedford and Tanya Firsova},
title = {Geometric proof of the $\lambda ${-Lemma}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {1--18},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 25},
number = {1},
year = {2016},
doi = {10.5802/afst.1485},
zbl = {1341.30007},
mrnumber = {3485289},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1485/}
}
TY - JOUR AU - Eric Bedford AU - Tanya Firsova TI - Geometric proof of the $\lambda $-Lemma JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2016 SP - 1 EP - 18 VL - 25 IS - 1 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1485/ DO - 10.5802/afst.1485 LA - en ID - AFST_2016_6_25_1_1_0 ER -
%0 Journal Article %A Eric Bedford %A Tanya Firsova %T Geometric proof of the $\lambda $-Lemma %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2016 %P 1-18 %V 25 %N 1 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1485/ %R 10.5802/afst.1485 %G en %F AFST_2016_6_25_1_1_0
Eric Bedford; Tanya Firsova. Geometric proof of the $\lambda $-Lemma. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 25 (2016) no. 1, pp. 1-18. doi : 10.5802/afst.1485. https://afst.centre-mersenne.org/articles/10.5802/afst.1485/
[1] Astala (K.) and Martin (G.J.).— Holomorphic motions, Report. Univ. Jyväskylä 83, p. 27-40 (2001). | Zbl
[2] Bedford (E.).— Stability of the polynomial hull of , Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 8, no. 2, p. 311-315 (1981).
[3] Bedford (E.) and Gaveau (B.).— Envelopes of holomorphy of certain 2-spheres in , Amer. J. Math. 105, p. 975-1009 (1983). | DOI | MR | Zbl
[4] Bedford (E.) and Klingenberg (W.).— On the envelope of holomorphy of a 2-sphere in , J. Amer. Math. Soc. 3, p. 623-646 (1991). | DOI | MR | Zbl
[5] Bers (L.) and Royden (H.).— Holomorphic families of injections, Acta Math. 157, p. 259-286 (1986). | DOI | MR | Zbl
[6] Bishop (E.).— Differentiable manifolds in complex Euclidean space, Duke Math. J. 32, p. 1-21 (1965). | DOI | MR | Zbl
[7] Chirka (E.M.).— On the propagation of holomorphic motions, Dokl. Akad. Nauk 397(1), p. 37-40 (2004). | Zbl
[8] Cielebak (K.) and Eliashberg (Y.).— From Stein to Weistein and back. Symplectic geometry of affine complex manifolds, American Mathematical Society Colloquium Publications, vol. 59, Am. Math. Soc. (2012).
[9] Earle (C.J.) and Kra (I.).— On holomorphic mappings between Teichmüller spaces, Contributions to Analysis, Academic Press (New York), p. 107-124 (1974). | DOI
[10] Forstnerič (F.).— Polynomial hulls of sets that fiber over the circle, Indiana Univ. Math. J 37, p. 869-889 (1988). | DOI | Zbl
[11] Greenfield (S.) and Wallach (N.).— Extendibility properties of submanifolds of , Proc. Carolina Conf. on Holo-morphic Mappings and Minimal Surfaces (Chapel Hill, N.C.), p. 77-85 (1970).
[12] Hubbard (J. H.).— Sur les sections analytiques de la courbe universelle de Teichmüller, Mem. Am. Math. Soc. 4 (1976). | DOI | MR | Zbl
[13] Hubbard (J. H.).— Teichmüller theory and applications to geometry, topology and dynamics, Vol. 1, Matrix Editions (2006). | Zbl
[14] Lyubich (M.).— Some typical properties of the dynamics of rational maps, Russian Math. Surveys 38, p. 154-155 (1983). | Zbl
[15] Mañé (R.), Sad (P.), and Sullivan (D.).— On the dynamics of rational maps, Ann. Sci. École Norm. Sup. 16, p. 193-217 (1983). | DOI | MR | Zbl
[16] Słodkowski (Z.).— Holomorphic motions and polynomial hulls, Proc. Amer. Math Society 111, p. 347-355 (1991). | DOI | MR | Zbl
[17] Sullivan (D.) and Thurston (W.).— Extending holomorphic motions, Acta Math 157, p. 243-257 (1986). | DOI | MR | Zbl
[18] Šnirelman (A.I.).— The degree of a quasiruled mapping and the nonlinear Hilbert problem, Mat.Sb. (N.S.) 89(131), p. 366-389 (1972). | DOI
Cited by Sources: