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Complex Manifolds and Hyperbolic Geometry
Edited by: Clifford J. Earle, Cornell University, Ithaca, NY, William J. Harvey, King's College, London, England, and Sevín Recillas-Pishmish, Instituto de Matematicas, UNAM, Morelia, Mexico

Contemporary Mathematics
2002; 343 pp; softcover
Volume: 311
ISBN-10: 0-8218-2957-2
ISBN-13: 978-0-8218-2957-8
List Price: US$103
Member Price: US$82.40
Order Code: CONM/311
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This volume derives from the second Iberoamerican Congress on Geometry, held in 2001 in Mexico at the Centro de Investigación en Matemáticas A.C., an internationally recognized program of research in pure mathematics. The conference topics were chosen with an eye toward the presentation of new methods, recent results, and the creation of more interconnections between the different research groups working in complex manifolds and hyperbolic geometry. This volume reflects both the unity and the diversity of these subjects.

Researchers around the globe have been working on problems concerning Riemann surfaces, as well as a wide scope of other issues: the theory of Teichmüller spaces, theta functions, algebraic geometry and classical function theory.

Included here are discussions revolving around questions of geometry that are related in one way or another to functions of a complex variable. There are contributors on Riemann surfaces, hyperbolic geometry, Teichmüller spaces, and quasiconformal maps.

Complex geometry has many applications--triangulations of surfaces, combinatorics, ordinary differential equations, complex dynamics, and the geometry of special curves and jacobians, among others. In this book, research mathematicians in complex geometry, hyperbolic geometry and Teichmüller spaces will find a selection of strong papers by international experts.


Research mathematicians and graduate students in complex geometry, hyperbolic geometry and Teichmüller spaces.

Table of Contents

  • A. M. Bonifant and M. Dabija -- Self-maps of \({\mathbb P}^2\) with invariant elliptic curves
  • J. F. Brock -- Pants decompositions and the Weil-Petersson metric
  • A. Carocca, S. Recillas, and R. E. Rodríguez -- Dihedral groups acting on Jacobians
  • C. J. Earle -- Schwarz's lemma and Teichmüller contraction
  • C. J. Earle, V. Markovic, and D. Saric -- Barycentric extension and the Bers embedding for asymptotic Teichmüller space
  • A. L. Epstein -- Symmetric rigidity for real polynomials with real critical points
  • H. M. Farkas and I. Kra -- On theta constant identities and the evaluation of trigonometric sums
  • A. Gamburd and E. Makover -- On the genus of a random Riemann surface
  • F. P. Gardiner, J. Hu, and N. Lakic -- Earthquake curves
  • F. P. Gardiner and N. Lakic -- Efficient smooth quasiconformal mappings
  • T. M. Gendron -- The Ehrenpreis conjecture and the moduli-rigidity gap
  • J. Gilman and L. Keen -- Word sequences and intersection numbers
  • L. Giraldo and X. Gómez-Mont -- A law of conservation of number for local Euler characteristics
  • G. González-Díez and W. J. Harvey -- On families of algebraic curves with automorphisms
  • R. A. Hidalgo -- Real surfaces, Riemann matrices and algebraic curves
  • N. Lakic and S. Mitra -- Approximation by meromorphic quadratic differentials
  • B. Maskit -- On the topology of classical Schottky space
  • R. Silhol -- Hyperbolic lego and algebraic curves in genus 2 and 3
  • P. Susskind -- The Margulis region and continued fractions
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