Geometry and Spectra of Compact Riemann Surfaces

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 op...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Buser, Peter (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Boston : Birkhäuser Boston, 2010.
Σειρά:Modern Birkhäuser Classics
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03999nam a22005055i 4500
001 978-0-8176-4992-0
003 DE-He213
005 20151204150034.0
007 cr nn 008mamaa
008 110222s2010 xxu| s |||| 0|eng d
020 |a 9780817649920  |9 978-0-8176-4992-0 
024 7 |a 10.1007/978-0-8176-4992-0  |2 doi 
040 |d GrThAP 
050 4 |a QA440-699 
072 7 |a PBM  |2 bicssc 
072 7 |a MAT012000  |2 bisacsh 
082 0 4 |a 516  |2 23 
100 1 |a Buser, Peter.  |e author. 
245 1 0 |a Geometry and Spectra of Compact Riemann Surfaces  |h [electronic resource] /  |c by Peter Buser. 
264 1 |a Boston :  |b Birkhäuser Boston,  |c 2010. 
300 |a XIV, 456 p. 145 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Modern Birkhäuser Classics 
505 0 |a 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. 
520 |a 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. 
650 0 |a Mathematics. 
650 0 |a Algebra. 
650 0 |a Algebraic geometry. 
650 0 |a Functions of complex variables. 
650 0 |a Geometry. 
650 1 4 |a Mathematics. 
650 2 4 |a Geometry. 
650 2 4 |a Several Complex Variables and Analytic Spaces. 
650 2 4 |a Algebraic Geometry. 
650 2 4 |a Algebra. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9780817649913 
830 0 |a Modern Birkhäuser Classics 
856 4 0 |u http://dx.doi.org/10.1007/978-0-8176-4992-0  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)