Completeness of the Bergman metric on non-smooth pseudoconvex domains

Bo-Yong Chen

Annales Polonici Mathematici (1999)

  • Volume: 71, Issue: 3, page 241-251
  • ISSN: 0066-2216

Abstract

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We prove that the Bergman metric on domains satisfying condition S is complete. This implies that any bounded pseudoconvex domain with Lipschitz boundary is complete with respect to the Bergman metric. We also show that bounded hyperconvex domains in the plane and convex domains in ℂ n are Bergman comlete.

How to cite

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Bo-Yong Chen. "Completeness of the Bergman metric on non-smooth pseudoconvex domains." Annales Polonici Mathematici 71.3 (1999): 241-251. <http://eudml.org/doc/262778>.

@article{Bo1999,
abstract = {We prove that the Bergman metric on domains satisfying condition S is complete. This implies that any bounded pseudoconvex domain with Lipschitz boundary is complete with respect to the Bergman metric. We also show that bounded hyperconvex domains in the plane and convex domains in $ℂ^n$ are Bergman comlete.},
author = {Bo-Yong Chen},
journal = {Annales Polonici Mathematici},
keywords = {Bergman metric; condition S; pseudoconvexity; hyperconvexity; Bergman completeness; pluricomplex Green function; -equation on complete Kähler manifolds; Kähler metric},
language = {eng},
number = {3},
pages = {241-251},
title = {Completeness of the Bergman metric on non-smooth pseudoconvex domains},
url = {http://eudml.org/doc/262778},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Bo-Yong Chen
TI - Completeness of the Bergman metric on non-smooth pseudoconvex domains
JO - Annales Polonici Mathematici
PY - 1999
VL - 71
IS - 3
SP - 241
EP - 251
AB - We prove that the Bergman metric on domains satisfying condition S is complete. This implies that any bounded pseudoconvex domain with Lipschitz boundary is complete with respect to the Bergman metric. We also show that bounded hyperconvex domains in the plane and convex domains in $ℂ^n$ are Bergman comlete.
LA - eng
KW - Bergman metric; condition S; pseudoconvexity; hyperconvexity; Bergman completeness; pluricomplex Green function; -equation on complete Kähler manifolds; Kähler metric
UR - http://eudml.org/doc/262778
ER -

References

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