Abstract
In [L1], Lempert studied the properties of the infinitesimal Kobayashi metric on smoothly bounded strongly convex domains in ℂn. He showed that the exponential map for the infinitesimal Kobayashi metric (which is a Finsler metric) is a smooth diffeomorphism from the tangent space minus the origin onto the domain minus the base point; moreover, if the map is suitably renormalized, then the map restricts to any complex line through the origin as a biholomorphic map from a unit (Kobayashi) disc in the tangent line onto a proper holomorphic curve in the domain. He also realized that this map could be used for the analysis of the equivalence classes of pointed domains. In [L2], he discussed normal forms for domains along the boundary of extremal discs, and produced analytic modular data for the class of pointed framed convex domains.
1980 Mathematics Subject Classification (1985 Revision). 32 H 15
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© 1991 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Bland, J., Duchamp, T. (1991). Circular Models and Normal Forms for Convex Domains. In: Diederich, K. (eds) Complex Analysis. Aspects of Mathematics, vol 1. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86856-5_8
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DOI: https://doi.org/10.1007/978-3-322-86856-5_8
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