ON THE HIGHER ORDER KOBAYASHI METRICS

  • KIM, JONG JIN (Department of Mathematics, Chonbuk National University) ;
  • HWANG, IN GYU (Department of Mathematics, Chonju University) ;
  • KIM, JEONG GYUN (Department of Mathematics, Chonbuk National University) ;
  • LEE, JEONG SEUNG (Department of Mathematics, Chonbuk National University)
  • Received : 2004.07.01
  • Published : 2004.12.25

Abstract

In this paper, we prove the product property and the existence of an extremal analytic disc relative to the higher order Kobayashi metric. Also by making use of the upper semicontinuity of the higher order Kobayashi metric, we introduce a pseudodistance and investigate some properties of that pseudodistance related to the usual Kobayashi metric.

Keywords

higher order Kobayashi metric;taut;pseudodistance

Acknowledgement

Supported by : Chonbuk National University

References

  1. Geometric analysis on weakly pseudoconvex domains Yu, J.
  2. Acta Math. Hungar v.90 no.4 Stability and boundary behavior of the Kobayashi metrics Nikolov, N.
  3. Pacific J. Math. v.162 On infinitesimal Behavior of the Kobayashi distance Pang, M.Y.
  4. Proceedings of the Maryland Conference on Several Complex Variables II Remarkes on the Kobayashi metric;Lecture Notes in Math. 189 Royden, H.L.
  5. Trans. AMS. v.207 Boundary behavior of the Caratheodory and Kobayashi metrics on Strongly Pseudoconvex Domains in $C^n$ with smooth boundary Graham, I.
  6. Invariant distances and Metrics in Complex Analysis Jarnicki, M.;Pflug, P.
  7. Hyperbolic manifolds and Holomorphic mappings Kobayashi, S.
  8. Bull. Soc. Math. France v.109 La metrique de Kobayashi et la representation des domaines sur la boule Lempert, L.