Geometry of Riemann Surfaces

Original research and expert surveys on Riemann surfaces.

Frederick P. Gardiner (Edited by), Gabino González-Diez (Edited by), Christos Kourouniotis (Edited by)

9780521733076, Cambridge University Press

Paperback, published 11 February 2010

416 pages, 51 b/w illus.
22.9 x 15.2 x 2.4 cm, 0.61 kg

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.

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. González-Aguilera
Non-special divisors supported on the branch set of a p-gonal Riemann surface G. González-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.

Subject Areas: Differential & Riemannian geometry [PBMP]