The Kobayashi indicatrix at the center of a circular domain

Barth, Theodore J.

doi:10.1090/S0002-9939-1983-0699426-0

The Kobayashi indicatrix at the center of a circular domain
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by Theodore J. Barth PDF

Proc. Amer. Math. Soc. 88 (1983), 527-530 Request permission

Abstract:

The indicatrix of the Kobayashi infinitesimal metric at the center of a pseudoconvex complete circular domain coincides with this domain. It follows that a nonconvex complete circular domain cannot be biholomorphic to any convex domain. An example shows that a bounded pseudoconvex complete circular domain in ${{\mathbf {C}}^2}$ need not be taut.

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Über die Geometrie der analytischen Abbildungen, die durch analytische Funktionen von zwei Veränderlichen vermittelt werden

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