Geometry of Riemann Surfaces

Geometry of Riemann Surfaces

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Riemann surfaces is a thriving area of mathematics with applications to hyperbolic geometry, complex analysis, fractal geometry, conformal dynamics, discrete groups, geometric group theory, algebraic curves and their moduli, various kinds of deformation theory, coding, thermodynamic formalism, and topology of three-dimensional manifolds. This collection of articles, authored by leading authorities in the field, comprises 16 expository essays presenting original research and expert surveys of important topics related to Riemann surfaces and their geometry. It complements the body of recorded research presented in the primary literature by broadening, re-working and extending it in a more focused and less formal framework, and provides a valuable commentary on contemporary work in the subject. An introductory section sets the scene and provides sufficient background to allow graduate students and research workers from other related areas access to the field.
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Product details

  • Online resource
  • Cambridge, United Kingdom
  • English
  • 51 b/w illus.
  • 1139194267
  • 9781139194266

Table of contents

Preface; Foreword W. J. Harvey; Semisimple actions of mapping class groups on CAT(0) spaces M. R. Bridson; A survey of research inspired by Harvey's theorem on cyclic groups of automorphisms E. Bujalance, F. J. Cirre and G. Gromadzki; Algorithms for simple closed geodesics P. Buser; Matings in holomorphic dynamics S. Bullett; Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 4 A. F. Costa and M. Izquierdo; Diffeomorphisms and automorphisms of compact hyperbolic 2-orbifolds C. J. Earle; Holomorphic motions and related topics F. P. Gardiner, Y. Jiang and Z. Wang; Cutting sequences and palindromes J. Gilman and L. Keen; On a Schottky problem for the singular locus of A5 V. Gonzalez-Aguilera; Non-special divisors supported on the branch set of a p-gonal Riemann surface G. Gonzalez-Diez; A note on the lifting of automorphisms R. Hidalgo and B. Maskit; Simple closed geodesics of equal length on a torus G. McShane and H. Parlier; On extensions of holomorphic motions - a survey S. Mitra; Complex hyperbolic quasi-Fuchsian groups J. R. Parker and I. D. Platis; Geometry of optimal trajectories M. Pontani and P. Teofilatto; Actions of fractional Dehn twists on moduli spaces R. Silhol.
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About Frederick P. Gardiner

Frederick P. Gardiner is Broeklundian Professor in the Department of Mathematics at Brooklyn College, CUNY. Gabino Gonzalez-Diez is Professor in the Department of Mathematics at the Autonomous University of Madrid. Christos Kourouniotis is Assistant Professor in the Department of Mathematics at the University of Crete.
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