Jensen measures and unbounded B-regular domains in {\mathbf{C}}^n

Nguyen, Quang Dieu; Hung, Dau Hoang

doi:10.5802/aif.2388

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Cited by 2 publications

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“…Finally, we point out that in the paper [8], the authors considered (non necessarily continuous) bounded above psh. functions φ defined on some unbounded domains in C n and having the property lim z →∞ φ(z) = −∞ with the aim to study a Dirichlet type problem on some family of unbounded domains.…”

Section: Remarkmentioning

confidence: 99%

Unbounded Kobayashi hyperbolic domains in $\mathbb C^n$

Gaussier¹,

Shcherbina²

2019

Preprint

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We first give a sufficient condition, issued from pluripotential theory, for an unbounded domain in the complex Euclidean space C n to be Kobayashi hyperbolic. Then, we construct an example of a rigid pseudoconvex domain in C 3 that is Kobayashi hyperbolic and has a nonempty core. In particular, this domain is not biholomorphic to a bounded domain in C 3 and the mentioned above sufficient condition for Kobayashi hyperbolicity is not necessary.

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Section: Remarkmentioning

confidence: 99%