Abstract: We consider two problems for holomorphic maps into convex domains in ℂn. The first is to give conditions under which a holomorphic map which is an isometry for the infinitesimal Kobayashi metric at one point must be biholomorphic. The second is to estimate the distortion for a holomorphic map into a convex domain in terms of a readily computable quantity, namely the radii of certain linear discs in the domain and target space of the map. (In problem 2 the domain of the mapping is another domain in ℂn.) This leads to estimates for the Kobayashi metric on convex domains, and a version of the Koebe theorem. Sharp constants have now been obtained for these results [G5].
Publication Year: 1991
Publication Date: 1991-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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