Mathematische Zeitschrift

, Volume 232, Issue 1, pp 183–196

The Bergman metric on hyperconvex domains


  • Gregor Herbort
    • Fachbereich Mathematik, Bergische Universität-Gesamthochschule Wuppertal, Gaußstraße 20, D-42097 Wuppertal, Germany
Original article

DOI: 10.1007/PL00004754

Cite this article as:
Herbort, G. Math Z (1999) 232: 183. doi:10.1007/PL00004754


In this article it is shown that the Bergman metric on a bounded hyperconvex domain in \(\mathbb{C}^n\) is always complete. A counterexample demonstrates, that the converse conclusion fails in general.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999