Włodarczyk: Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains

Włodarczyk, Kazimierz:
Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains (Rigidità di applicazioni olomorfe e distorsione di applicazioni biolomorfe in domini di Siegel)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 6 (1995), fasc. n.3, p. 185-197, (English)
pdf (1.24 MB), djvu (291 Kb). | MR1363786 | Zbl 0840.46028

Sunto

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.

Referenze Bibliografiche

[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 1120709 | Zbl 0737.32005

[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. | fulltext (doi) | MR 1250815 | Zbl 0814.32004

[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. | fulltext (doi) | MR 1242454 | Zbl 0807.32008

[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 0011.12302

[6] J. M. COHEN - F. COLONNA, Bounded holomorphic functions on bounded symmetric domains. Trans. Amer. Math. Soc., 343, 1994, 135-156. | fulltext (doi) | MR 1176085 | Zbl 0804.32018

[7] S. DINEEN, The Schwarz Lemma. Oxford Mathematical Monographs, Clarendon Press, Oxford 1989. | MR 1033739 | Zbl 0708.46046

[8] P. DUREN - W. RUDIN, Distortion in several variables. Complex Variables Theory Appl., 5, 1986, 323-326. | MR 846500 | Zbl 0559.32004

[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 1300835 | Zbl 0812.32003

[10] T. FRANZONI - E. VESENTINI, Holomorphic Maps and Invariant Distances. North-Holland Mathematics Studies, 40, Amsterdam-New York-Oxford 1980. | MR 563329 | Zbl 0447.46040

[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 1242200 | Zbl 0788.32017

[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 1220063 | Zbl 0781.32005

[13] I. GRAHAM, Distortion theorems for holomorphic maps between convex domains in \( C^{n} \). Complex Variables Theory Appl., 15, 1990, 37-42. | MR 1055937 | Zbl 0681.32002

[14] L. A. HARRIS, Schwarz's lemma in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A., 62, 1969, 1014-1017. | MR 275179 | Zbl 0199.19401

[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 305037 | Zbl 0199.18302

[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 407330 | Zbl 0293.46049

[17] L. A. HARRIS, On the size of balls covered by analytic transformations. Monatsh. Math., 83, 1977, 9-23. | fulltext EuDML | MR 435454 | Zbl 0356.46046

[18] L. A. HARRIS, Operator Siegel domains. Proc. Roy. Soc. Edinburgh, 79 A, 1977, 137-156. | MR 484600 | Zbl 0376.32027

[19] L. A. HARRIS, Linear fractional transformations of circular domains in operator spaces. Indiana Univ. Math. J., 41, 1992, 125-147. | fulltext (doi) | MR 1160906 | Zbl 0760.47018

[20] M. HERVÉ, Lindelöfs Principle in Infinite Dimensions. Lecture Notes in Mathematics, 364, Springer-Verlag, Berlin-Heidelberg-New York 1974, 41-57. | MR 393587 | Zbl 0272.58003

[21] M. HERVÉ, Some Properties of the Images of Analytic Maps. North-Holland Mathematics Studies 12, Amsterdam-New York-Oxford 1977, 217-229. | MR 492403 | Zbl 0373.46050

[22] M. HERVÉ, Analyticity in Infinite Dimensional Spaces. de Gruyter Studies in Mathematics, 10, Berlin-New York 1989. | fulltext (doi) | MR 986066 | Zbl 0666.58008

[23] Y. KUBOTA, Some results on rigidity of holomorphic mappings. Kodai Math. J., 17, 1994, 246-255. | fulltext mini-dml | fulltext (doi) | MR 1282213 | Zbl 0817.32012

[24] I. I. PJATECKIJ-SHAPIRO, Automorphic Functions and the Geometry of Classical Domains. Gordon-Breach, New York 1969. | MR 252690 | Zbl 0196.09901

[25] C. H. POMMERENKE, Univalent Functions. Vandenhoeck and Ruprecht, Göttingen 1975. | MR 507768 | Zbl 0298.30014

[26] W. RUDIN, Functional Analysis. McGraw-Hill, New York 1973. | MR 365062 | Zbl 0867.46001

[27] W. RUDIN, Function Theory in the Unit Ball of \( C^{n} \). Springer-Verlag, New York-Heidelberg-Berlin 1980. | MR 601594 | Zbl 1139.32001

[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 450601 | Zbl 0356.32004

[29] E. VESENTINI, Rigidity of holomorphic isometries. Rend. Mat. Acc. Lincei, s. 9, vol. 5, 1994, 55-62. | fulltext bdim | MR 1273893 | Zbl 0802.46059

[30] K. WZODARCZYK, On holomorphic maps in Banach spaces and \( J^{*} \)-algebras. Quart. J. Math. Oxford, (2), 36, 1985, 495-511. | fulltext (doi) | MR 816489 | Zbl 0595.46048

[31] K. WZODARCZYK, Hyperbolic geometry in bounded symmetric homogeneous domains of \( J^{*} \)-algebras. Atti Sem. Mat. Fis. Univ. Modena, 39, 1991, 201-211. | MR 1111769 | Zbl 0744.46035

[32] K. WZODARCZYK, Fixed points and invariant domains of expansive holomorphic maps in complex Banach spaces. Adv. in Math., 110, 1995, 247-254. | fulltext (doi) | MR 1317617 | Zbl 0868.47036

[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 1274084 | Zbl 0823.30014

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche