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Lipa's Legacy
Edited by: Józef Dodziuk and Linda Keen, City University of New York, New York City

Contemporary Mathematics
1997; 479 pp; softcover
Volume: 211
ISBN-10: 0-8218-0671-8
ISBN-13: 978-0-8218-0671-5
List Price: US$87
Member Price: US$69.60
Order Code: CONM/211
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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.


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


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

Table of Contents

  • W. Abikoff and T. Ye -- Computing the Douady-Earle extension
  • A. Basmajian -- Selected problems in Kleinian groups and hyperbolic geometry
  • C. J. Bishop and P. W. Jones -- The law of the iterated logarithm for Kleinian groups
  • I. Biswas and S. Nag -- Weil-Petersson geometry and determinant bundles on inductive limits of moduli spaces
  • J. F. Brock -- Iteration of mapping classes on a Bers slice: examples of algebraic and geometric limits of hyperbolic 3-manifolds
  • C. Cao, F. W. Gehring, and G. J. Martin -- Lattice constants and a lemma of Zagier
  • Y. Chiang -- The quasi-Fuchsian space of four-punctured spheres
  • J. Dodziuk and V. Mathai -- Approximating \(L^2\) invariants of amenable covering spaces: A heat kernel approach
  • T. Dubejko -- Random walks on circle packings
  • C. J. Earle -- Some maximal holomorphic motions
  • C. J. Earle, F. P. Gardiner, and N. Lakic -- Vector fields for holomorphic motions of closed sets
  • H. M. Farkas and I. Kra -- Theta constant identities with applications to combinatorial number theory
  • D. M. Gallo -- The topology of real projective structures
  • J. Gilman -- A discreteness condition for subgroups of \(PSL(2,{\mathbf C})\)
  • V. González-Aguilera and R. E. Rodríguez -- On principally polarized abelian varieties and Riemann surfaces associated to prisms and pyramids
  • A. Hinkkanen -- Schur products of certain polynomials
  • Y. E. Hohlov and D. Y. Kleinbock -- Inverse problems for fluid flows with a moving boundary
  • Y. Jiang -- On rigidity of one-dimensional maps
  • Y. Katznelson and D. S. Ornstein -- Twist maps and Aubry-Mather sets
  • L. Keen and C. Series -- How to bend pairs of punctured tori
  • I. Kra and B. Maskit -- Lipman Bers, complex analyst
  • N. Lakic -- Strebel points
  • B. Maskit -- Remarks on \(m\)-symmetric Riemann surfaces
  • G. D. Mostow -- Quasi-conformal mappings of Carnot-Caratheodory spaces
  • L. Nirenberg -- Lipman Bers and partial differential equations
  • D. J. Pinchbeck -- Irrational rotations
  • U. Srebro and E. Yakubov -- \(\mu\)-homeomorphisms
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