rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Geometry and Spectra of Compact Riemann Surfaces
  name:
    name part: Buser, Peter.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2010
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 456 p. 145 illus. online resource.
  abstract: 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.
  table of contents: 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.
  note: by Peter Buser.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Algebraic geometry
  subject:
    topic: Functions of complex variables
  subject:
    topic: Geometry
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: Several Complex Variables and Analytic Spaces
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Algebra
  classification: QA440-699
  classification: 516
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Modern Birkhäuser Classics
  identifier: 9780817649920
  identifier: http://dx.doi.org/10.1007/978-0-8176-4992-0
  record info:
    record creation date: 110222
    record change date: 20151204150034.0
    record identifier: 978-0-8176-4992-0