000			03934nam a22004815i 4500
001			978-0-8176-4992-0
003			DE-He213
005			20140220084458.0
007			cr nn 008mamaa
008			110222s2010 xxu| s |||| 0|eng d
020			_a9780817649920 _9978-0-8176-4992-0
024	7		_a10.1007/978-0-8176-4992-0 _2doi
050		4	_aQA331.7
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.94 _223
100	1		_aBuser, Peter. _eauthor.
245	1	0	_aGeometry and Spectra of Compact Riemann Surfaces _h[electronic resource] / _cby Peter Buser.
264		1	_aBoston : _bBirkhäuser Boston, _c2010.
300			_aXVIII, 474p. 145 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aModern Birkhäuser Classics
505	0		_aHyperbolic 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			_aThis 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	_aMathematics.
650		0	_aAlgebra.
650		0	_aGeometry, algebraic.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aAlgebraic Geometry.
650	2	4	_aAlgebra.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817649913
830		0	_aModern Birkhäuser Classics
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-8176-4992-0
912			_aZDB-2-SMA
999			_c109932 _d109932