Skip to main content
SpringerLink
Log in
Birkhäuser

Geometry and Spectra of Compact Riemann Surfaces

  • Book
  • © 2010

Overview

Authors:
  1. Peter Buser

    1. , Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne-Ecublens, Switzerland

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Modern Birkhäuser Classics (MBC)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Hyperbolic Structures

    • Peter Buser
    Pages 1-30

  3. Trigonometry

    • Peter Buser
    Pages 31-62

  4. Y-Pieces and Twist Parameters

    • Peter Buser
    Pages 63-93

  5. The Collar Theorem

    • Peter Buser
    Pages 94-121

  6. Bers’ Constant and the Hairy Torus

    • Peter Buser
    Pages 122-137

  7. The Teichmüller Space

    • Peter Buser
    Pages 138-181

  8. The Spectrum of the Laplacian

    • Peter Buser
    Pages 182-209

  9. Small Eigenvalues

    • Peter Buser
    Pages 210-223

  10. Closed Geodesics and Huber’s Theorem

    • Peter Buser
    Pages 224-267

  11. Wolpert’s Theorem

    • Peter Buser
    Pages 268-282

  12. Sunada’s Theorem

    • Peter Buser
    Pages 283-310

  13. Examples of Isospectral Riemann Surfaces

    • Peter Buser
    Pages 311-339

  14. The Size of Isospectral Families

    • Peter Buser
    Pages 340-361

  15. Perturbations of the Laplacian in Teichmüller Space

    • Peter Buser
    Pages 362-408

  16. Back Matter

    Pages 409-456
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

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 Răileanu, 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)

Authors and Affiliations

  • , Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne-Ecublens, Switzerland

    Peter Buser

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation