1995
DOI: 10.2307/2118631
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An Estimate for the Bergman Distance on Pseudoconvex Domains

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Cited by 68 publications
(43 citation statements)
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“…Theorem 6.2 does not give any quantitative version of this, even in terms of pluripotential theory. Diederich and Ohsawa [49] showed a lower bound for the Bergman distance for bounded pseudoconvex domains with C 2 boundary implying in particular completeness, this was later improved in [23]:…”
Section: Theorem 64 Bounded Hyperconvex Domains Are Bergman Exhaustivementioning
confidence: 99%
“…Theorem 6.2 does not give any quantitative version of this, even in terms of pluripotential theory. Diederich and Ohsawa [49] showed a lower bound for the Bergman distance for bounded pseudoconvex domains with C 2 boundary implying in particular completeness, this was later improved in [23]:…”
Section: Theorem 64 Bounded Hyperconvex Domains Are Bergman Exhaustivementioning
confidence: 99%
“…[4], [5], [6], [12], [13], [14], [15], [17], [20]). On the other hand, Diederich and Ohsawa [10] proved that the Bergman distance for a bounded C 2 pseudoconvex domain in C n has a lower bound of a constant multiple log | log δ Ω |. This lower bound was improved by Blocki [3] to | log δ Ω |/ log | log δ Ω |.…”
Section: Theoremmentioning
confidence: 99%
“…Following an idea of [10], we will show Lemma 3. There exists a sufficiently large constant b such that for any y ∈ Ω satisfying |ρ(y)| < 2 −e , we have…”
mentioning
confidence: 99%
“…Ohsawa also found several interesting applications of the Donnelly-Fefferman estimate, for instance, to the Hodge theory on singular complex spaces and to the study of the Bergman metric (cf. [16], [5] etc). The main result in [8] is H p,q 2 (M ) = 0 for p + q = n and dim H p,q 2 (M ) = ∞ for p + q = n, associated to the Bergman metric on bounded strongly pesudoconvex domains.…”
mentioning
confidence: 99%