Hyperbolicity in unbounded convex domains

DOI10.1515/FORUM.2009.039zbMath1183.32014arXiv0704.0751MaRDI QIDQ3182455

Alberto Saracco, Filippo Bracci

Publication date: 9 October 2009

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0704.0751

zbMATH Keywords

Bergman metricKobayashi pseudodistanceunbounded convex domainantipeak plurisubharmonic functionpeak plurisubharmonic functiontaut domain

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Normal families of holomorphic functions, mappings of several complex variables, and related topics (taut manifolds etc.) (32A19) Analytical consequences of geometric convexity (vanishing theorems, etc.) (32F32) Peak functions (32T40)

Related Items (14)

Gromov hyperbolicity of pseudoconvex finite type domains in \(\mathbb{C}^2\) ⋮ Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type ⋮ Complex geodesics in convex tube domains. II ⋮ Hyperbolic imbeddedness and tautness modulo a closed subset ⋮ Regularity of complex geodesics and (non-)Gromov hyperbolicity of convex tube domains ⋮ Nonlinear resolvents and decreasing Loewner chains ⋮ Homeomorphic extension of quasi-isometries for convex domains in \(\mathbb{C}^d\) and iteration theory ⋮ The space of convex domains in complex Euclidean space ⋮ Carathéodory and Kobayashi hyperbolicity of unbounded domains in ℂⁿ ⋮ Discrete sequences in unbounded domains ⋮ Invariant holomorphic foliations on Kobayashi hyperbolic homogeneous manifolds ⋮ Fridman function, injectivity radius function, and squeezing function ⋮ Kobayashi hyperbolic convex domains not biholomorphic to bounded convex domains ⋮ Flexible domains for minimal surfaces in Euclidean spaces

Cites Work

• Holomorphic retracts and intrinsic metrics in convex domains
• Proper holomorphic discs avoiding closed convex sets
• Convex Domains and Kobayashi Hyperbolicity
• Tautness and complete hyperbolicity of domains in $\mathbb {C}^n$
• Estimates for the Bergman kernel and metric of convex domains in Cⁿ
• Behavior of the Bergman kernel and metric near convex boundary points
• On the relations between taut, tight and hyperbolic manifolds

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