Kleinian group


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Kleinian group

[′klī·nē·ən ‚grüp]
(mathematics)
A group of conformal mappings of a Riemann surface onto itself which is discontinuous at one or more points and is not discontinuous at more than two points.
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It also is proved that a Kleinian group [GAMMA] has a generating set consisting of elements whose traces are real ([14, Theorem 6.
For the sake of completeness, we record in Section 2 some fundamentals on hyperbolic geometry, fundamental domains and on Fuchsian and Kleinian groups.
By Theorem I (and II) of [Su], there is no invariant measurable tangent line field on the conservative part of the action of any Kleinian group on [Mathematical Expression Omitted].
They discuss topics related to Kleinian groups, classical Riemann surface theory, mapping class groups, geometric group theory, and statistical mechanics.
Sharing his appreciation for the beauty of such mathematical objects as Kleinian groups and hyperbolic knots, Bonahon (University of Southern California) first introduces 2-dimensional geometry in chapters of incremental difficulty.
Kleinian Groups and Hyperbolic 3-Manifolds workshop (201: Warwick) Ed.
Patterson, Measures on limit sets of Kleinian groups, Analytical and Geometric Aspects of Hyperbolic Spaces, Cambridge University Press, Cambridge, U.
The topics include Bers and partial differential equations, measurable Riemann mappings, the Ahlfor-Bers creation of the modern theory of Kleinian groups, the Bers embeddings and (some of) its ramifications, the Weil-Petersson geometry of a family of Riemann surfaces, and the early history of moduli and TeichmEller spaces.