Holomorphic Functions and Moduli II

1. Front Matter

   Pages i-xiii

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2. Fuchsian Groups

   1. Mostow rigidity on the line: A survey

      • Stephen Agard

      Pages 1-12

   2. Fuchsian groups and n ^th roots of parabolic generators

      • A. F. Beardon

      Pages 13-22

   3. On the existence of elliptics in subgroups of PSL(2, ℝ): A graphical picture

      • Jane Gilman

      Pages 23-27

   4. The kernel of the Poincaré series operator of weight -2

      • Makoto Masumoto

      Pages 29-40

3. Kleinian Groups and Generalizations

   1. Strange actions of groups on spheres, II

      • Michael H. Freedman, Richard Skora

      Pages 41-57

   2. Quasiconformal groups and the conical limit set

      • J. B. Garnett, F. W. Gehring, P. W. Jones

      Pages 59-67

   3. Generic fundamental polyhedra for kleinian groups

      • T. Jorgensen, A. Marden

      Pages 69-85

   4. Quasiconformal Actions on Domains in Space

      • Gaven J. Martin

      Pages 87-111

   5. Convergence and Möbius Groups

      • Gaven J. Martin, Pekka Tukia

      Pages 113-140

   6. The limit set of a discrete group of hyperbolic motions

      • Peter J. Nicholls

      Pages 141-164

   7. A remark on a paper by Floyd

      • Pekka Tukia

      Pages 165-172

   8. Purely elliptic Möbius groups

      • P. L. Waterman

      Pages 173-178

4. Teichmüller Spaces

   1. Conformally natural reflections in Jordan curves with applications to Teichmüller spaces

      • Clifford J. Earle, Subhashis Nag

      Pages 179-194

   2. A theorem of Bers and Greenberg for infinite dimensional Teichmüller spaces

      • Frederick P. Gardiner

      Pages 195-205

   3. A finiteness theorem for holomorphic families of Riemann surfaces

      • Yoighi Imayoshi, Hiroshige Shiga

      Pages 207-219

   4. Non-variational global coordinates for Teichmüller spaces

      • Irwin Kra

      Pages 221-249

   5. Parameters for Fuchsian Groups I: Signature (0, 4)

      • Bernard Maskit

      Pages 251-265

   6. Parametrization of Teichmüller spaces by geodesic length functions

      • Mika Seppälä, Tuomas Sorvali

      Pages 267-284

   7. Families of compact Riemann surfaces which do not admit n ^th roots

      • Patricia L. Sipe

      Pages 285-290

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.

• Riemann surface
• convergence
• distribution
• holomorphic function
• operator
• quasiconformal mapping

• Department of Mathematics, Purdue University, West Lafayette, USA

  D. Drasin

• Mathematical Sciences Research Institute, Berkeley, USA

  D. Drasin, C. J. Earle, F. W. Gehring, I. Kra, A. Marden

• Department of Mathematics, Cornell University, Ithaca, USA

  C. J. Earle

• Department of Mathematics, University of Michigan, Ann Arbor, USA

  F. W. Gehring

• Department of Mathematics, State University of New York at Stony Brook, Stony Brook, USA

  I. Kra

• Department of Mathematics, University of Minnesota, Minneapolis, USA

  A. Marden

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