**Contemporary Mathematics**

Volume: 211;
1997;
479 pp;
Softcover

MSC: Primary 30; 32; 35;

**Print ISBN: 978-0-8218-0671-5
Product Code: CONM/211**

List Price: $98.00

AMS Member Price: $78.40

MAA Member Price: $88.20

**Electronic ISBN: 978-0-8218-7803-3
Product Code: CONM/211.E**

List Price: $92.00

AMS Member Price: $73.60

MAA Member Price: $82.80

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# Lipa’s Legacy

Share this page *Edited by *
*Józef Dodziuk; Linda Keen*

The mathematical works of Lars Ahlfors and Lipman Bers are
fundamental and lasting. They have influenced and altered the
development of twentieth century mathematics. The personalities of
these two scientists helped create a mathematical family and have had
a permanent positive effect on a whole generation of
mathematicians. Their mathematical heritage continues to lead
succeeding generations. In the fall of 1994, one year after Bers'
death, some members of this family decided to inaugurate a series of
conferences, The Bers Colloquium, to be held every three
years. The theme was to be a topic in the Ahlfors-Bers mathematical
tradition, broadly interpreted. Ahlfors died a year after the first
colloquium; future colloquia in this series will be called The
Ahlfors-Bers Colloquium.

The first colloquium was held in October 1995 at the Graduate
Center, CUNY in New York. It coincided roughly with the second
anniversary of Bers' death. There were six lectures and much informal
mathematical discussion. This volume contains papers by the speakers
and many of the participants. The broad range of papers indicates how
strong and far-reaching Bers' influence has been. The topics
represented in the book include Teichmüller theory, Kleinian
groups, higher dimensional hyperbolic geometry, geometry of numbers,
circle packings, theory of discrete groups, classical complex function
theory, one dimensional dynamics, fluid dynamics, quasiconformal
mappings in higher dimensions, partial differential equations, and
classical algebraic geometry.

Features:

- Twenty-seven very high-level papers on related topics
- Open problems
- Expository articles

#### Readership

Graduate students and research mathematicians interested in functions of a complex variable, and related areas of mathematics.

# Table of Contents

## Lipa's Legacy

- Contents v6 free
- Preface vii8 free
- Computing the Douady-Earle extension 110 free
- Selected problems in Kleinian groups and hyperbolic geometry 918
- The law of the iterated logarithm for Kleinian groups 1726
- Weil-Petersson geometry and determinant bundles on inductive limits of moduli spaces 5160
- Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic 3-manifolds 8190
- Lattice constants and a lemma of Zagier 107116
- The quasi-Fuchsian space of four-punctured spheres 121130
- Approximating L2 invariants of amenable covering spaces: A heat kernel approach 151160
- Random walks on circle packings 169178
- Some maximal holomorphic motions 183192
- Vector fields for holomorphic motions of closed sets 193202
- Theta constant identities with applications to combinatorial number theory 227236
- The topology of real projective structures 253262
- A discreteness condition for subgroups of PSL(2, C) 261270
- On principally polarized abelian varieties and Riemann surfaces associated to prisms and pyramids 269278
- Schur products of certain polynomials 285294
- Inverse problems for fluid flows with a moving boundary 297306
- On rigidity of one-dimensional maps 319328
- Twist maps and Aubry-Mather sets 343352
- How to bend pairs of punctured tori 359368
- Lipman Bers, complex analyst 389398
- Strebel points 417426
- Remarks on m-symmetric Riemann surfaces 433442
- Quasi-conformal mappings of Carnot-Caratheodory spaces 447456
- Lipman Bers and partial differential equations 455464
- Irrational rotations 463472
- μ-homeomorphisms 473482