Bergman minimal domains in several complex variables
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- by Shigeo Ozaki and Sadao Katô
- Trans. Amer. Math. Soc. 162 (1971), 63-69
- DOI: https://doi.org/10.1090/S0002-9947-1971-0294695-X
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Abstract:
K. T. Hahn has obtained the inequality between the Jacobians of a biholomorphic mapping and a holomorphic automorphism of a Bergman minimal domain. This paper extends Hahn’s result. Some inequalities concerning Jacobians of the mappings of minimal domains onto another minimal domain are considered, and an example is given.References
- Stefan Bergmann, Sur les fonctions orthogonales de plusieurs variables complexes avec les applications à la théorie des fonctions analytiques, Mémor. Sci. Math., no. 106, Gauthier-Villars, Paris, 1947 (French). MR 0032776 —, Sur la fonction-noyau d’un domaine et ses applications dans la théorie des transformations pseudo-conformes, Mémor. Sci. Math., no. 108, Gauthier-Villars, Paris, 1948. MR 11, 344.
- Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR 0038439
- K. T. Hahn and Josephine Mitchell, Generalization of Schwarz-Pick lemma to invariant volume in a Kähler manifold, Trans. Amer. Math. Soc. 128 (1967), 221–231. MR 243120, DOI 10.1090/S0002-9947-1967-0243120-2
- Kyong T. Hahn, Some properties of relative invariants on bounded domains, Duke Math. J. 34 (1967), 325–332. MR 214809 S. Katō, Theorems in several complex variables, Rep. Fac. Tech. Kanagawa Univ. 4 (1965), 7-27.
- Sadao Kató, Canonical domains in several complex variables, Pacific J. Math. 21 (1967), 279–291. MR 214810
- Sadao Kató, Mitchell minimal domains in several complex variables, Duke Math. J. 37 (1970), 139–143. MR 254266
- Michael Maschler, Minimal domains and their Bergman kernel function, Pacific J. Math. 6 (1956), 501–516. MR 81951
- Shigeo Ozaki and Isao Onô, Analytic functions of several complex variables, Sci. Rep. Tokyo Bunrika Daigaku. Sect. A 4 (1953), 262–270. MR 56714
- Teruo Tsuboi, Bergman representative domains and minimal domains, Jpn. J. Math. 29 (1959), 141–148. MR 121504, DOI 10.4099/jjm1924.29.0_{1}41
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 162 (1971), 63-69
- MSC: Primary 32H05
- DOI: https://doi.org/10.1090/S0002-9947-1971-0294695-X
- MathSciNet review: 0294695