English

The Kobayashi metric, extremal discs, and biholomorphic mappings

Complex Variables 2009-09-08 v1

Abstract

We study extremal discs for the Kobayashi metric. Inspired by work of Lempert on strongly convex domains, we present results on strongly pseudoconvex domains. We also consider a useful biholomorphic invariant, inspired by the Kobayashi (and Carath\'{e}odory) metric, and prove several new results about biholomorphic equivalence of domains. Some useful results about automorphism groups of complex domains are also established.

Keywords

Cite

@article{arxiv.0909.1041,
  title  = {The Kobayashi metric, extremal discs, and biholomorphic mappings},
  author = {Steven G. Krantz},
  journal= {arXiv preprint arXiv:0909.1041},
  year   = {2009}
}