Ebook: Holomorphic Functions and Moduli II: Proceedings of a Workshop held March 13–19, 1986

The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe­ maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a mini-conference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici­ pants. These volumes represent only a portion of the papers that will even­ tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program­ whether or not they gave a talk at the Workshop. Papers were also submit­ ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref­ erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup­ porting the Program in GFT. Finally thanks are due to the National Sci­ ence Foundation and those Universities (including Cornell, Michigan, Min­ nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program.

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Content:
Front Matter....Pages i-xiii
Mostow rigidity on the line: A survey....Pages 1-12
Fuchsian groups and n th roots of parabolic generators....Pages 13-22
On the existence of elliptics in subgroups of PSL(2, ?): A graphical picture....Pages 23-27
The kernel of the Poincar? series operator of weight -2....Pages 29-40
Strange actions of groups on spheres, II....Pages 41-57
Quasiconformal groups and the conical limit set....Pages 59-67
Generic fundamental polyhedra for kleinian groups....Pages 69-85
Quasiconformal Actions on Domains in Space....Pages 87-111
Convergence and M?bius Groups....Pages 113-140
The limit set of a discrete group of hyperbolic motions....Pages 141-164
A remark on a paper by Floyd....Pages 165-172
Purely elliptic M?bius groups....Pages 173-178
Conformally natural reflections in Jordan curves with applications to Teichm?ller spaces....Pages 179-194
A theorem of Bers and Greenberg for infinite dimensional Teichm?ller spaces....Pages 195-205
A finiteness theorem for holomorphic families of Riemann surfaces....Pages 207-219
Non-variational global coordinates for Teichm?ller spaces....Pages 221-249
Parameters for Fuchsian Groups I: Signature (0, 4)....Pages 251-265
Parametrization of Teichm?ller spaces by geodesic length functions....Pages 267-284
Families of compact Riemann surfaces which do not admit n th roots....Pages 285-290

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Content:
Front Matter....Pages i-xiii
Mostow rigidity on the line: A survey....Pages 1-12
Fuchsian groups and n th roots of parabolic generators....Pages 13-22
On the existence of elliptics in subgroups of PSL(2, ?): A graphical picture....Pages 23-27
The kernel of the Poincar? series operator of weight -2....Pages 29-40
Strange actions of groups on spheres, II....Pages 41-57
Quasiconformal groups and the conical limit set....Pages 59-67
Generic fundamental polyhedra for kleinian groups....Pages 69-85
Quasiconformal Actions on Domains in Space....Pages 87-111
Convergence and M?bius Groups....Pages 113-140
The limit set of a discrete group of hyperbolic motions....Pages 141-164
A remark on a paper by Floyd....Pages 165-172
Purely elliptic M?bius groups....Pages 173-178
Conformally natural reflections in Jordan curves with applications to Teichm?ller spaces....Pages 179-194
A theorem of Bers and Greenberg for infinite dimensional Teichm?ller spaces....Pages 195-205
A finiteness theorem for holomorphic families of Riemann surfaces....Pages 207-219
Non-variational global coordinates for Teichm?ller spaces....Pages 221-249
Parameters for Fuchsian Groups I: Signature (0, 4)....Pages 251-265
Parametrization of Teichm?ller spaces by geodesic length functions....Pages 267-284
Families of compact Riemann surfaces which do not admit n th roots....Pages 285-290
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