The generalized Schwarz lemma for the Bergman metric
Copyright policy )The generalized Schwarz lemma for the Bergman metric
The author provides a function-theoretic criterion for the Bergman metric to be dominated by the Kobayashi metric on domains of \({\mathbb{C}}^ n\). The criterion is based on a distinguished family of plurisubharmonic functions and a P-metric of N. Sibony, and on a family of biholomorphic invariant functions induced by the Bergman kernel of the domain, introduced by the reviewer in Proc. Conf., Princeton Univ. 1979, Ann. Math. Stud. 65-92 (1981; Zbl 0469.32010).
- University of Toyama Japan
32H15, Bergman metric, Kobayashi metric, Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, Carathéodory metric, Integral representations; canonical kernels (Szegő, Bergman, etc.), Schwarz lemma, Other generalizations of function theory of one complex variable, 32H10, Invariant metrics and pseudodistances in several complex variables, Hyperbolic and Kobayashi hyperbolic manifolds
32H15, Bergman metric, Kobayashi metric, Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, Carathéodory metric, Integral representations; canonical kernels (Szegő, Bergman, etc.), Schwarz lemma, Other generalizations of function theory of one complex variable, 32H10, Invariant metrics and pseudodistances in several complex variables, Hyperbolic and Kobayashi hyperbolic manifolds
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