Geometry and Spectra of Compact Riemann Surfaces

• Hyperbolic Structures.- Trigonometry.- Y-Pieces and Twist Parameters.- The Collar Theorem.- Bers’ Constant and the Hairy Torus.- The Teichmüller Space.- The Spectrum of the Laplacian.- Small Eigenvalues.- Closed Geodesics and Huber’s Theorem.- Wolpert’s Theorem.- Sunada’s Theorem.- Examples of Isospectral Riemann Surfaces.- The Size of Isospectral Families.- Perturbations of the Laplacian in Teichmüller Space.

From the reviews: "Anyone familiar with the author's hands-on approach to Riemann surfaces will be gratified by both the breadth and the depth of the topics considered here. The exposition is also extremely clear and thorough. Anyone not familiar with the author's approach is in for a real treat." -Mathematical Reviews "Originally published as Volume 106 in the series Progress in Mathematics, this version is a reprint of the classic monograph, 1992 edition, consisting of two parts. ... An appendix is devoted to curves and isotopies. The book is a very useful reference for researches and also for graduate students interested in the geometry of compact Riemann surfaces of constant curvature -- 1 and their length and eigenvalue spectra." (Liliana Raileanu, Zentralblatt MATH, Vol. 1239, 2012) "Geometry and Spectra of Compact Riemann Surfaces is a pleasure to read. There is a lot of motivation given, examples proliferate, propositions and theorems come equipped with clear proofs, and excellent drawings ... . a fine piece of scholarship and a pedagogical treat." (Michael Berg, The Mathematical Association of America, May, 2011)