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

 Access to full text

 Full (PDF)

 Full (DjVu)

1. BARNARD, R. W. - FITZGERALD, C. H. - GONG, S., The growth and $1/4$-theorems for starlike functions in $C^n$. Pacific J. Math., 150, 1991, 13-22. Zbl0737.32005MR1120709
2. BARNARD, R. W. - FITZGERALD, C. H. - GONG, S., A distortion theorem for biholomorphic mappings in $C^2$. Trans. Amer. Math. Soc., 344, 1994, 907-924. Zbl0814.32004MR1250815DOI10.2307/2154515
3. BURNS, D. M. - KRANTZ, S., Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary. J. Amer. Math. Soc., 7, 1994, 661-676. Zbl0807.32008MR1242454DOI10.2307/2152787
4. CARTAN, H., 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, Paris1933, 129-155. JFM59.0344.01
5. CARTAN, E., Sur les domaines bornés homogènes de l'espace de n variables complexes. Abh. Math. Sem. Univ. Hamburg, 11, 1935, 116-162. Zbl0011.12302
6. COHEN, J. M. - COLONNA, F., Bounded holomorphic functions on bounded symmetric domains. Trans. Amer. Math. Soc., 343, 1994, 135-156. Zbl0804.32018MR1176085DOI10.2307/2154525
7. DINEEN, S., The Schwarz Lemma. Oxford Mathematical Monographs, Clarendon Press, Oxford1989. Zbl0708.46046MR1033739
8. DUREN, P. - RUDIN, W., Distortion in several variables. Complex Variables Theory Appl., 5, 1986, 323-326. Zbl0559.32004MR846500
9. FITZGERALD, C. H. - THOMAS, C. R., Some bounds on convex mappings in several complex variables. Pacific J. Math., 165, 1994, 295-320. Zbl0812.32003MR1300835
10. FRANZONI, T. - VESENTINI, E., Holomorphic Maps and Invariant Distances. North-Holland Mathematics Studies, 40, Amsterdam-New York-Oxford 1980. Zbl0447.46040MR563329
11. GONG, S. - WANG, S. K. - YU, Q. H., Biholomorphic convex mappings of ball in $C^n$. Pacific J. Math., 161, 1993, 287-306. Zbl0788.32017MR1242200
12. GONG, S. - WANG, S. K. - YU, Q. H., The growth theorem for biholomorphic mappings in several complex variables. Chinese Ann. Math., Ser. B 14, 1993, 93-104. Zbl0781.32005MR1220063
13. GRAHAM, I., Distortion theorems for holomorphic maps between convex domains in $C^n$. Complex Variables Theory Appl., 15, 1990, 37-42. Zbl0681.32002MR1055937
14. HARRIS, L. A., Schwarz's lemma in normed linear spaces. Proc. Nat. Acad. Sci. U.S.A., 62, 1969, 1014-1017. Zbl0199.19401MR275179
15. HARRIS, L. A., A continuous form of Schwarz's lemma in normed linear spaces. Pacific J. Math., 38, 1971, 635-639. Zbl0199.18302MR305037
16. HARRIS, L. A., Bounded Symmetric Homogeneous Domains in Infinite Dimensional Spaces. Lecture Notes in Mathematics, 364, Springer-Verlag, Berlin-Heidelberg-New York1974, 13-40. Zbl0293.46049MR407330
17. HARRIS, L. A., On the size of balls covered by analytic transformations. Monatsh. Math., 83, 1977, 9-23. Zbl0356.46046MR435454
18. HARRIS, L. A., Operator Siegel domains. Proc. Roy. Soc. Edinburgh, 79 A, 1977, 137-156. Zbl0376.32027MR484600
19. HARRIS, L. A., Linear fractional transformations of circular domains in operator spaces. Indiana Univ. Math. J., 41, 1992, 125-147. Zbl0760.47018MR1160906DOI10.1512/iumj.1992.41.41008
20. HERVÉ, M., Lindelöfs Principle in Infinite Dimensions. Lecture Notes in Mathematics, 364, Springer-Verlag, Berlin-Heidelberg-New York1974, 41-57. Zbl0272.58003MR393587
21. HERVÉ, M., Some Properties of the Images of Analytic Maps. North-HollandMathematics Studies12, Amsterdam-New York-Oxford1977, 217-229. Zbl0373.46050MR492403
22. HERVÉ, M., Analyticity in Infinite Dimensional Spaces. de GruyterStudies in Mathematics, 10, Berlin-New York1989. Zbl0666.58008MR986066DOI10.1515/9783110856941
23. KUBOTA, Y., Some results on rigidity of holomorphic mappings. Kodai Math. J., 17, 1994, 246-255. Zbl0817.32012MR1282213DOI10.2996/kmj/1138039963
24. PJATECKIJ-SHAPIRO, I. I., Automorphic Functions and the Geometry of Classical Domains. Gordon-Breach, New York1969. Zbl0196.09901MR252690
25. POMMERENKE, C. H., Univalent Functions. Vandenhoeck and Ruprecht, Göttingen1975. Zbl0298.30014MR507768
26. RUDIN, W., Functional Analysis. McGraw-Hill, New York1973. Zbl0867.46001MR365062
27. RUDIN, W., Function Theory in the Unit Ball of $C^n$. Springer-Verlag, New York-Heidelberg-Berlin1980. Zbl1139.32001MR601594
28. SUFFRIDGE, T. J., Starlikeness, Convexity and other Geometric Properties of Holomorphic Maps in Higher Dimensions. Lecture Notes in Mathematics, 599, Springer-Verlag, New York1976, 146-159. Zbl0356.32004MR450601
29. VESENTINI, E., Rigidity of holomorphic isometries. Rend. Mat. Acc. Lincei, s. 9, vol. 5, 1994, 55-62. Zbl0802.46059MR1273893
30. WZODARCZYK, K., On holomorphic maps in Banach spaces and $J^{*}$-algebras. Quart. J. Math. Oxford, (2), 36, 1985, 495-511. Zbl0595.46048MR816489DOI10.1093/qmath/36.4.495
31. WZODARCZYK, K., Hyperbolic geometry in bounded symmetric homogeneous domains of $J^{*}$-algebras. Atti Sem. Mat. Fis. Univ. Modena, 39, 1991, 201-211. Zbl0744.46035MR1111769
32. WZODARCZYK, K., Fixed points and invariant domains of expansive holomorphic maps in complex Banach spaces. Adv. in Math., 110, 1995, 247-254. Zbl0868.47036MR1317617DOI10.1006/aima.1995.1010
33. YAMASHITA, S., The Pick version of the Schwarz lemma and comparison of the Poincaré densities. Ann. Acad. Sci. Fenn., 19, 1994, 291-322. Zbl0823.30014MR1274084