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MARC 21

Geometry and Spectra of Compact Riemann Surfaces
Tag	Description
020	$a9780817649920
082	$a515.223
099	$aOnline Resource: Birkhäuser
100	$aBuser, Peter.$d1946-
245	$aGeometry and Spectra of Compact Riemann Surfaces$h[Ebook]$cby Peter Buser.
250	$aReprint of the 1992 edition
260	$aBoston$bBirkhäuser$c2010.
300	$aXVIII, 474 pages, 145 illus.$bonline resource.
336	$atext
338	$aonline resource
440	$aModern Birkhäuser Classics
505	$aPreface.-Chapter 1: Hyperbolic Structures.-Chapter 2: Trigonometry -- Chapter 3: Y-Pieces and Twist Parameters -- Chapter 4:The Collar Theorem -- Chapter 5: Bersâ Constant and the Hairy Torus -- Chapter 6: The Teichmüller Space -- Chapter 7: The Spectrum of the Laplacian -- Chapter 8: Small Eigenvalues -- Chapter 9: Closed Geodesics and Huberâs Theorem -- Chapter 10: Wolpertâs Theorem -- Chapter 11: Sunadaâs Theorem -- Chapter 12: Examples of Isospectral Riemann surfaces -- Chapter 13: The Size of Isospectral Families -- Chapter 14: Perturbations of the Laplacian in Hilbert Space.-Appendix: Curves and Isotopies.-Bibliography.-Index.-Glossary.
520	$aThis classic monograph is a self-contained introduction to the geometry of Riemann surfaces of constant curvature â1 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, Sunadaâs construction, a simplified proof of Wolpertâs 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. Â 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. â Mathematical ReviewsÂ This is a thick and leisurely book which will repay repeated study with many pleasant hours â 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 âstate of the artâ in the theory of the LaplaceâBeltrami operator on compact Riemann surfaces. Although it is not encyclopedic, it is so rich in information and ideas â¦ the reader will be grateful for what has been included in this very satisfying book. âBulletin of the AMS Â The book is very well written and quite accessible; there is an excellent bibliography at the end. âZentralblatt MATH
538	$aOnline access is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aModern Birkhäuser Classics
856	$uhttp://dx.doi.org/10.1007/978-0-8176-4992-0