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Riemann mappings of invariant components of Kleinian groups
Author(s) -
Shiga Hiroshige
Publication year - 2009
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdp052
Subject(s) - kleinian group , invariant (physics) , mathematics , bounded function , pure mathematics , riemann hypothesis , riemann surface , fuchsian group , mathematical analysis , mathematical physics
In this paper, we shall investigate complex analytic properties of Riemann mappings of simply connected invariant components of Kleinian groups. In particular, we consider the growth of the derivatives of Riemann mappings to understand Kleinian groups that are quasi‐Fuchsian groups, regular b ‐groups and Kleinian groups with bounded geometry.