Steven G. Krantz
Published 2009-09-05Version 1
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.
A form of Schwarz's lemma and a bound for the Kobayashi metric on convex domains
Gromov hyperbolicity, the Kobayashi metric, and $\mathbb{C}$-convex sets
Quasi-isometries in strongly convex domains
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