**Contemporary Mathematics**

Volume: 432;
2007;
229 pp;
Softcover

MSC: Primary 14; 20; 28; 30; 32; 54; 57;

Print ISBN: 978-0-8218-4227-0

Product Code: CONM/432

List Price: $86.00

Individual Member Price: $68.80

**Electronic ISBN: 978-0-8218-8111-8
Product Code: CONM/432.E**

List Price: $86.00

Individual Member Price: $68.80

# In the Tradition of Ahlfors-Bers, IV

Share this page *Edited by *
*Dick Canary; Jane Gilman; Juha Heinonen; Howard Masur*

The Ahlfors–Bers Colloquia commemorate the mathematical legacy of Lars Ahlfors and Lipman Bers. The core of this legacy lies in the fields of geometric function theory, Teichmüller theory, hyperbolic manifolds, and partial differential equations. However, the work of Ahlfors and Bers has impacted and created interactions with many other fields, such as algebraic geometry, mathematical physics, dynamics, geometric group theory, number theory, and topology. The triannual Ahlford–Bers colloquia serve as a venue to disseminate the relevant work to the wider mathematical community and bring the key participants together to ponder future directions in the field.

The present volume includes a wide range of articles in the fields central to this legacy. The majority of articles present new results, but there are expository articles as well.

#### Table of Contents

# Table of Contents

## In the Tradition of Ahlfors-Bers, IV

- Contents v6 free
- Preface vii8 free
- Plenary Talks ix10 free
- Workshops and Workshop Speakers xi12 free
- Colloquium Participants xiii14 free
- Uniformly exponential growth and mapping class groups of surfaces 118 free
- An A1 weight not comparable with any quasiconformal Jacobian 724
- Curvature, stretchiness, and dynamics 1936
- Some special loci in the Siegel space of genus two 3148
- Another approach to the automorphism theorem for Teichmüller spaces 3956
- Energy of twisted harmonic maps of Riemann surfaces 4562
- Introduction 4663
- Acknowledgments 4764
- Notation and Terminology 4764
- 1. Flat bundles and harmonic maps 4865
- 2. Bounded geometry 4966
- 3. Existence of harmonic maps 5067
- 4. The action of Diff(S) on Ts 5168
- 5. Properness of the energy function 5370
- 6. Action of the mapping class group 5572
- 7. Accidental parabolics 5673
- 8. When G = PSL(2, C) 5875
- 9. Speculation 5875
- References 6077

- Isometries of some hyperbolic-type path metrics, and the hyperbolic medial axis 6380
- From left earthquakes to right 7592
- Small eigenvalues and maximal laminations on complete surfaces of negative curvature 93110
- A generalized hyperbolic metric for plane domains 107124
- Subgroups of mapping class groups from the geometrical viewpoint 119136
- Determinants of Laplacians, quasifuchsian spaces, and holomorphic extensions of Laplacians 143160
- Hyperbolic and quasisymmetric structure of hyperspace 151168
- A classification of the modular transformations of infinite dimensional Teichmüller spaces 167184
- Random hyperbolic surfaces and measured laminations 179196
- Extensions of holomorphic motions to quasiconformal motions 199216
- Analyst's Traveling Salesman Theorems. A Survey 209226
- Energy of harmonic maps and Gardiner's formula 221238

#### Readership

Graduate students and research mathematicians interested in geometric function theory.