Extremal plurisubharmonic functions and invariant pseudodistances

DOI10.24033/bsmf.2029zbMath0584.32037OpenAlexW2584856073MaRDI QIDQ3709090

Maciej Klimek

Publication date: 1985

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1985__113__231_0

zbMATH Keywords

complex Monge-Ampère equationgeneralized Green's functionextremal plurisubharmonic functionCarathéodory-Kobayashi pseudodistanceLindelöf property of Green's functions

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Holomorphic mappings and correspondences (32H99) Pluriharmonic and plurisubharmonic functions (31C10) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20) Plurisubharmonic functions and generalizations (32U05)

Related Items (39)

Boundary behavior of extremal plurisubharmonic functions ⋮ Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures) ⋮ Approximation of plurisubharmonic functions by multipole Green functions ⋮ Estimates of the Bergman kernel on Teichmüller space ⋮ The Bergman metric on a Stein manifold with a bounded plurisubharmonic function ⋮ The invariant pseudo-metric related to negative plurisubharmonic functions ⋮ Behavior of Invariant Metrics Near Convexifiable Boundary Points ⋮ The Dirichlet problem with prescribed interior singularities ⋮ Bergman Kernel in Complex Analysis ⋮ On Stein manifolds M for which \({\mathcal O}(M)\) is isomorphic to \({\mathcal O}(\Delta^ n)\) as Fréchet spaces ⋮ Envelopes with prescribed singularities ⋮ Schwarz lemmas via the pluricomplex Green's function ⋮ The Green function of Teichmüller spaces with applications ⋮ Weighted Green functions for complex Hessian operators ⋮ A Property of upper level sets of Lelong numbers of currents on ℙ2 ⋮ Boundary behavior of the Bergman metric ⋮ Non-linearity of the pluricomplex Green function ⋮ Monge-Ampère measures on subvarieties ⋮ The Dirichlet problem for the complex homogeneous Monge-Ampère equation ⋮ Pluricomplex Green functions on manifolds ⋮ Uniqueness of complex geodesics and characterization of circular domains ⋮ Cauchy–Riemann meet Monge–Ampère ⋮ Proof of a conjecture of Zahariuta concerning a problem of Kolmogorov on the \(\epsilon\)-entropy ⋮ Compactness of the \(\overline{\partial} \)-Neumann problem on domains with bounded intrinsic geometry ⋮ Plurisubharmonic functions with logarithmic singularities ⋮ Transcendental versions in \(\mathbb{C}^n\) of the Nagata conjecture ⋮ Pluripotential theory on Teichmüller space I: Pluricomplex Green function ⋮ Old and new invariant pseudo-distances defined by pluriharmonic functions ⋮ On subextension of pluriharmonic and plurisubharmonic functions ⋮ Bounds for invariant distances on pseudoconvex Levi corank one domains and applications ⋮ Teichmüller Theory, Thurston Theory, Extremal Length Geometry and Complex Analysis ⋮ Boundary behavior of the pluricomplex Green function ⋮ On Extension Properties of Pluricomplex Green Functions ⋮ Quantitative estimates for the Green function and an application to the Bergman metric ⋮ (Pluri)potential compactifications ⋮ Quasiplurisubharmonic Green functions ⋮ Monge-Ampère measures on pluripolar sets ⋮ Estimation on invariant distances on pseudoconvex domains of finite type in dimension two ⋮ A note on Carathéodory and Kobayashi pseudodistances

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• A new capacity for plurisubharmonic functions
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• Holomorphic retracts and intrinsic metrics in convex domains
• Analytic functions in circular rings
• Extremal plurisubharmonic functions in $C^N$
• La métrique de Kobayashi et la représentation des domaines sur la boule
• The Caratheodory Metric of the Annulus

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