Geometry and spectra of compact Riemann surfaces
著者
書誌事項
Geometry and spectra of compact Riemann surfaces
（Modern Birkhäuser classics）
Birkhäuser, c2010
Reprint of the 1992 ed
- : pbk
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注記
"Orignaly published as Volume 106 in the series Progress in Mathematics."--T.p. verso
Includes bibliographical references (p. [433]-447) and index
内容説明・目次
内容説明
This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature -1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.
目次
Hyperbolic Structures.- Trigonometry.- Y-Pieces and Twist Parameters.- The Collar Theorem.- Bers' Constant and the Hairy Torus.- The Teichmuller 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 Teichmuller Space.
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