Format:
Online-Ressource (XVIII, 474p. 145 illus, digital)
ISBN:
9780817649920
,
1283076101
,
9781283076104
Series Statement:
Modern Birkhäuser Classics
Content:
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.
Content:
This classic 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. The first part of the book is written in textbook form at the graduate level, with only minimal requisites in either differential geometry or complex Riemann surface theory. The second part of the book is a self-contained introduction to the spectrum of the Laplacian based on the heat equation. Later chapters deal with recent developments on isospectrality, Sunada’s construction, a simplified proof of Wolpert’s theorem, and an estimate of the number of pairwise isospectral non-isometric examples which depends only on genus. Researchers and graduate students interested in compact Riemann surfaces will find this book a useful reference. 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 This is a thick and leisurely book which will repay repeated study with many pleasant hours – both for the beginner and the expert. It is fortunately more or less self-contained, which makes it easy to read, and it leads one from essential mathematics to the “state of the art” in the theory of the Laplace–Beltrami operator on compact Riemann surfaces. Although it is not encyclopedic, it is so rich in information and ideas … the reader will be grateful for what has been included in this very satisfying book. —Bulletin of the AMS The book is very well written and quite accessible; there is an excellent bibliography at the end. —Zentralblatt MATH.
Note:
"Originally published as Volume 106 in the series Progress in mathematics"--T.p. verso
,
"Reprint of the 1992 edition
,
Includes bibliographical references (p. [433]-447) and index
,
Geometry and Spectra of Compact Riemann Surfaces; Preface; Contents; Chapter 1; Chapter 2; Chapter 3; Chapter 4; Chapter 5; Chapter 6; Chapter 7; Chapter 8; Chapter 9; Chapter 10; Chapter 11; Chapter 12; Chapter 13; Chapter 14; Appendix; Bibliography; Index; Formula Glossary
Additional Edition:
ISBN 9780817649913
Additional Edition:
Buchausg. u.d.T. ISBN 978-0-8176-4991-3
Additional Edition:
Erscheint auch als Druck-Ausgabe Buser, Peter, 1946 - Geometry and spectra of compact Riemann surfaces Boston : Birkhäuser, 1992 ISBN 0817634061
Additional Edition:
ISBN 3764334061
Language:
English
Subjects:
Mathematics
Keywords:
Kompakte Riemannsche Fläche
DOI:
10.1007/978-0-8176-4992-0
URL:
Volltext
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URL:
Volltext
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