Some remarks on the intrinsic measures of Eisenman

Graham, Ian; Wu, H.

doi:10.1090/S0002-9947-1985-0776396-4

Some remarks on the intrinsic measures of Eisenman
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by Ian Graham and H. Wu PDF

Trans. Amer. Math. Soc. 288 (1985), 625-660 Request permission

Abstract:

This paper studies the intrinsic measures on complex manifolds first introduced by Eisenman in analogy with the intrinsic distances of Kobayashi. Some standard conjectures, together with several new ones, are considered and partial or complete answers are provided. Most of the counterexamples come from a closer examination of unbounded domains in complex euclidean space. In particular, a large class of unbounded hyperbolic domains are exhibited. Those unbounded domains of finite euclidean volume are also singled out for discussion.

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Function theory on noncompact Kähler manifolds