Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 6 (1995) no. 3, pp. 185-197.

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Results concerning the rigidity of holomorphic maps and the distortion of biholomorphic maps in infinite dimensional Siegel domains of \( J^{*} \)-algebras are established. The homogeneity of the open unit balls in these algebras plays a key role in the arguments.
Si stabiliscono alcuni risultati sulla rigidità di applicazioni olomorfe e sulla distorsione di biolomorfismi di domini di Siegel di algebre \( J^{*} \). L'omogeneità dei dischi unità in queste algebre ha un ruolo essenziale nelle dimostrazioni.
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Włodarczyk, Kazimierz. Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 6 (1995) no. 3, pp. 185-197. http://geodesic.mathdoc.fr/item/RLIN_1995_9_6_3_a4/

[1] R. W. Barnard - C. H. Fitzgerald - S. Gong, The growth and \( 1/4 \)-theorems for starlike functions in \( C^{n} \). Pacific J. Math., 150, 1991, 13-22. | fulltext mini-dml | MR | Zbl

[2] R. W. Barnard - C. H. Fitzgerald - S. Gong, A distortion theorem for biholomorphic mappings in \( C^{2} \). Trans. Amer. Math. Soc., 344, 1994, 907-924. | DOI | MR | Zbl

[3] D. M. Burns - S. Krantz, Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary. J. Amer. Math. Soc., 7, 1994, 661-676. | DOI | MR | Zbl

[4] H. Cartan, Sur la possibilité d'étendre aux fonctions de plusieurs variables complexes la théorie des fonctions univalentes. Note added to P. MONTE, Leçons sur les fonctions Univalentes ou Multivalentes, Gauthier-Villars, Paris 1933, 129-155. | Jbk 59.0344.01

[5] E. Cartan, Sur les domaines bornés homogènes de l'espace de n variables complexes. Abh. Math. Sem. Univ. Hamburg, 11, 1935, 116-162. | Zbl

[6] J. M. Cohen - F. Colonna, Bounded holomorphic functions on bounded symmetric domains. Trans. Amer. Math. Soc., 343, 1994, 135-156. | DOI | MR | Zbl

[7] S. Dineen, The Schwarz Lemma. Oxford Mathematical Monographs, Clarendon Press, Oxford 1989. | MR | Zbl

[8] P. Duren - W. Rudin, Distortion in several variables. Complex Variables Theory Appl., 5, 1986, 323-326. | MR | Zbl

[9] C. H. Fitzgerald - C. R. Thomas, Some bounds on convex mappings in several complex variables. Pacific J. Math., 165, 1994, 295-320. | fulltext mini-dml | MR | Zbl

[10] T. Franzoni - E. Vesentini, Holomorphic Maps and Invariant Distances. North-Holland Mathematics Studies, 40, Amsterdam-New York-Oxford 1980. | MR | Zbl

[11] S. Gong - S. K. Wang - Q. H. Yu, Biholomorphic convex mappings of ball in \( C^{n} \). Pacific J. Math., 161, 1993, 287-306. | fulltext mini-dml | MR | Zbl

[12] S. Gong - S. K. Wang - Q. H. Yu, The growth theorem for biholomorphic mappings in several complex variables. Chinese Ann. Math., Ser. B 14, 1993, 93-104. | MR | Zbl

[13] I. Graham, Distortion theorems for holomorphic maps between convex domains in \( C^{n} \). Complex Variables Theory Appl., 15, 1990, 37-42. | MR | Zbl

[14] L. A. Harris, Schwarz's lemma in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A., 62, 1969, 1014-1017. | MR | Zbl

[15] L. A. Harris, A continuous form of Schwarz's lemma in normed linear spaces. Pacific J. Math., 38, 1971, 635-639. | fulltext mini-dml | MR | Zbl

[16] L. A. Harris, Bounded Symmetric Homogeneous Domains in Infinite Dimensional Spaces. Lecture Notes in Mathematics, 364, Springer-Verlag, Berlin-Heidelberg-New York 1974, 13-40. | MR | Zbl

[17] L. A. Harris, On the size of balls covered by analytic transformations. Monatsh. Math., 83, 1977, 9-23. | fulltext EuDML | MR | Zbl

[18] L. A. Harris, Operator Siegel domains. Proc. Roy. Soc. Edinburgh, 79 A, 1977, 137-156. | MR | Zbl

[19] L. A. Harris, Linear fractional transformations of circular domains in operator spaces. Indiana Univ. Math. J., 41, 1992, 125-147. | DOI | MR | Zbl

[20] M. Hervé, Lindelöfs Principle in Infinite Dimensions. Lecture Notes in Mathematics, 364, Springer-Verlag, Berlin-Heidelberg-New York 1974, 41-57. | MR | Zbl

[21] M. Hervé, Some Properties of the Images of Analytic Maps. North-Holland Mathematics Studies 12, Amsterdam-New York-Oxford 1977, 217-229. | MR | Zbl

[22] M. Hervé, Analyticity in Infinite Dimensional Spaces. de Gruyter Studies in Mathematics, 10, Berlin-New York 1989. | DOI | MR | Zbl

[23] Y. Kubota, Some results on rigidity of holomorphic mappings. Kodai Math. J., 17, 1994, 246-255. | fulltext mini-dml | DOI | MR | Zbl

[24] I. I. Pjateckij-Shapiro, Automorphic Functions and the Geometry of Classical Domains. Gordon-Breach, New York 1969. | MR | Zbl

[25] C. H. Pommerenke, Univalent Functions. Vandenhoeck and Ruprecht, Göttingen 1975. | MR | Zbl

[26] W. Rudin, Functional Analysis. McGraw-Hill, New York 1973. | MR | Zbl

[27] W. Rudin, Function Theory in the Unit Ball of \( C^{n} \). Springer-Verlag, New York-Heidelberg-Berlin 1980. | MR | Zbl

[28] T. J. Suffridge, Starlikeness, Convexity and other Geometric Properties of Holomorphic Maps in Higher Dimensions. Lecture Notes in Mathematics, 599, Springer-Verlag, New York 1976, 146-159. | MR | Zbl

[29] E. Vesentini, Rigidity of holomorphic isometries. Rend. Mat. Acc. Lincei, s. 9, vol. 5, 1994, 55-62. | fulltext bdim | MR | Zbl

[30] K. Wzodarczyk, On holomorphic maps in Banach spaces and \( J^{*} \)-algebras. Quart. J. Math. Oxford, (2), 36, 1985, 495-511. | DOI | MR | Zbl

[31] K. Wzodarczyk, Hyperbolic geometry in bounded symmetric homogeneous domains of \( J^{*} \)-algebras. Atti Sem. Mat. Fis. Univ. Modena, 39, 1991, 201-211. | MR | Zbl

[32] K. Wzodarczyk, Fixed points and invariant domains of expansive holomorphic maps in complex Banach spaces. Adv. in Math., 110, 1995, 247-254. | DOI | MR | Zbl

[33] S. Yamashita, The Pick version of the Schwarz lemma and comparison of the Poincaré densities. Ann. Acad. Sci. Fenn., 19, 1994, 291-322. | MR | Zbl