Bergman minimal domains in several complex variables

Ozaki, Shigeo; Katô, Sadao

doi:10.1090/S0002-9947-1971-0294695-X

Bergman minimal domains in several complex variables
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by Shigeo Ozaki and Sadao Katô PDF

Trans. Amer. Math. Soc. 162 (1971), 63-69 Request permission

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

11

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

Theorems in several complex variables

4

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