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Geometric proof of the λ-Lemma
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 1, pp. 1-18.

Nous donnons une approche géométrique de la preuve de la λ-lemma. Nous soulignons, en particulier, le rôle que la pseudoconvexité joue dans la preuve.

We give a geometric approach to the proof of the λ-lemma. In particular, we point out the role pseudoconvexity plays in the proof.

Reçu le : 2015-02-11
Accepté le : 2015-03-29
Publié le : 2016-02-29
DOI : https://doi.org/10.5802/afst.1485
@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},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 25},
     number = {1},
     year = {2016},
     pages = {1-18},
     doi = {10.5802/afst.1485},
     language = {en},
     url = {afst.centre-mersenne.org/item/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, Série 6, Tome 25 (2016) no. 1, pp. 1-18. doi : 10.5802/afst.1485. https://afst.centre-mersenne.org/item/AFST_2016_6_25_1_1_0/

[1] Astala (K.) and Martin (G.J.).— Holomorphic motions, Report. Univ. Jyväskylä 83, p. 27-40 (2001).

[2] Bedford (E.).— Stability of the polynomial hull of 𝕋 2 , 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 2 , Amer. J. Math. 105, p. 975-1009 (1983).

[4] Bedford (E.) and Klingenberg (W.).— On the envelope of holomorphy of a 2-sphere in 2 , J. Amer. Math. Soc. 3, p. 623-646 (1991).

[5] Bers (L.) and Royden (H.).— Holomorphic families of injections, Acta Math. 157, p. 259-286 (1986).

[6] Bishop (E.).— Differentiable manifolds in complex Euclidean space, Duke Math. J. 32, p. 1-21 (1965).

[7] Chirka (E.M.).— On the propagation of holomorphic motions, Dokl. Akad. Nauk 397(1), p. 37-40 (2004).

[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).

[10] Forstnerič (F.).— Polynomial hulls of sets that fiber over the circle, Indiana Univ. Math. J 37, p. 869-889 (1988).

[11] Greenfield (S.) and Wallach (N.).— Extendibility properties of submanifolds of 2 , 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).

[13] Hubbard (J. H.).— Teichmüller theory and applications to geometry, topology and dynamics, Vol. 1, Matrix Editions (2006).

[14] Lyubich (M.).— Some typical properties of the dynamics of rational maps, Russian Math. Surveys 38, p. 154-155 (1983).

[15] Mañé (R.), Sad (P.), and Sullivan (D.).— On the dynamics of rational maps, Ann. Sci. École Norm. Sup. 16, p. 193-217 (1983).

[16] Słodkowski (Z.).— Holomorphic motions and polynomial hulls, Proc. Amer. Math Society 111, p. 347-355 (1991).

[17] Sullivan (D.) and Thurston (W.).— Extending holomorphic motions, Acta Math 157, p. 243-257 (1986).

[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).