The Kobayashi metric, extremal discs, and biholomorphic mappings
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\'eodory) metric, and prove several new results about biholomorphic equivalence of domains. Some useful results about automorphism groups of complex domains are also established.
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