Geometry and Spectra of Compact Riemann Surfaces

(Autor)

Buch | Softcover
456 Seiten
2010 | Softcover reprint of hardcover edition 2010
Birkhauser Boston Inc (Verlag)
978-0-8176-4991-3 (ISBN)

Lese- und Medienproben

Geometry and Spectra of Compact Riemann Surfaces - Peter Buser
139,09 inkl. MwSt
This book deals with two subjects. The first subject is the geometric theory of compact Riemann surfaces of genus greater than one, the second subject is the Laplace operator and its relationship with the geometry of compact Riemann surfaces. The book grew out of the idea, a long time ago, to publish a Habili- tionsschrift, a thesis, in which I studied Bers' pants decomposition theorem and its applications to the spectrum of a compact Riemann surface. A basic tool in the thesis was cutting and pasting in connection with the trigono­ metry of hyperbolic geodesic polygons. As this approach to the geometry of a compact Riemann surface did not exist in book form, I took this book as an occasion to carry out the geometry in detail, and so it grew by several chapters. Also, while I was writing things up there was much progress in the field, and some of the new results were too challenging to be left out of the book. For instance, Sunada's construction of isospectral manifolds was fascinating, and I got hooked on constructing examples for quite a while. So time went on and the book kept growing. Fortunately, the interest in exis­ tence proofs also kept growing. The editor, for instance, was interested, and so was my family. And so the book finally assumed its present form. Many of the proofs given here are new, and there are also results which appear for the first time in print.

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.

Erscheint lt. Verlag 4.11.2010
Reihe/Serie Modern Birkhäuser Classics
Zusatzinfo 145 Illustrations, black and white; XIV, 456 p. 145 illus.
Verlagsort Secaucus
Sprache englisch
Maße 156 x 234 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-8176-4991-3 / 0817649913
ISBN-13 978-0-8176-4991-3 / 9780817649913
Zustand Neuware
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