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Title of Journal: Math Ann

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Abbravation: Mathematische Annalen

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Springer-Verlag

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10.1007/bf00610779

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1432-1807

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The Bergman metric on complete Kähler manifolds

Authors: BoYong Chen
Publish Date: 2003/08/13
Volume: 327, Issue: 2, Pages: 339-349
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Abstract

We use the existence of a bounded uniformly Hölder continuous plurisubharmonic exhaustion function to characterize the Bergman completeness of a complete Kähler manifold As an application we proved that any simplyconnected complete Kähler manifold with sectional curvature bounded above by a negative constant is Bergman complete

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  1. Estimates of the Green function for X-elliptic operators
  2. Fibred multilinks and singularities $${f \overline g}$$
  3. The NSLUC property and Klee envelope
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  5. Ricci flow on surfaces with cusps
  6. A non-laminar dynamical Green current
  7. Artin characters, Hurwitz trees and the lifting problem
  8. Generic non-selfadjoint Zakharov–Shabat operators
  9. Strichartz estimates via the Schrödinger maximal operator
  10. Examples of relative deformation spaces that are not locally connected
  11. Polynomial approximation of Berkovich spaces and definable types
  12. Prographes sylvestres et groupes profinis presque libres
  13. Zone diagrams in Euclidean spaces and in other normed spaces
  14. A critical radius for unit Hopf vector fields on spheres
  15. Many triangulated 3-spheres
  16. New examples of c 0 -saturated Banach spaces
  17. Rational curves, Dynkin diagrams and Fano manifolds with nef tangent bundle
  18. Relatively weakly open sets in closed balls of Banach spaces, and real JB * -triples of finite rank
  19. Conformal dimension via subcomplexes for small cancellation and random groups
  20. Analytic torsion of Hirzebruch surfaces
  21. Déformations des cônes de vecteurs primitifs
  22. Radial entire solutions for supercritical biharmonic equations
  23. Weighted Calderón–Zygmund and Rellich inequalities in $$L^p$$
  24. On entropy, regularity and rigidity for convex representations of hyperbolic manifolds
  25. Rigidity of proper holomorphic maps between bounded symmetric domains
  26. On CR Paneitz operators and CR pluriharmonic functions
  27. Absence of wandering domains for some real entire functions with bounded singular sets
  28. Isomonodromic deformations of logarithmic connections and stability
  29. Pointwise equidistribution with an error rate and with respect to unbounded functions
  30. On the Frobenius stable part of Witt vector cohomology
  31. Quantitative mixing results and inner functions
  32. Configuration spaces, transfer, and 2-nodal solutions of a semiclassical nonlinear Schrödinger equation
  33. Spin curves and Scorza quartics
  34. Points rationnels des variétés de Shimura: un principe du “tout ou rien”
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  37. On Oliver’s p -group conjecture: II
  38. Scattering in the energy space for the NLS with variable coefficients
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