论文信息 - Unbounded Kobayashi Hyperbolic Domains in C n

Unbounded Kobayashi Hyperbolic Domains in C n

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.

H. Gaussier | N. Shcherbina

[1] G. Tomassini,et al. On Defining Functions and Cores for Unbounded Domains II , 2020 .

[2] N. Shcherbina. On the existence of Kobayashi and Bergman metrics for Model domains , 2019, Mathematische Annalen.

[3] E. Poletsky,et al. Plurisubharmonically separable complex manifolds , 2017, Proceedings of the American Mathematical Society.

[4] G. Tomassini,et al. On defining functions and cores for unbounded domains I , 2017 .

[5] G. Tomassini,et al. Wermer type sets and extension of CR functions , 2010, 1006.1059.

[6] J. Fornæss,et al. A Construction of Peak Functions on Weakly Pseudoconvex Domains , 1978 .

[7] Z. Slodkowski. Pseudoconcave decompositions in complex manifolds , 2019, Advances in Complex Geometry.

[8] R. Krantz. TAUTNESS AND COMPLETE HYPERBOLICITY OF DOMAINS IN C , 1998 .

[9] N. Shcherbina. On the polynomial hull of a graph , 1993 .

[10] J. D'Angelo. Finite type conditions for real hypersurfaces , 1979 .

[11] Michel Hervé,et al. Classical potential theory , 1971 .