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This 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. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.
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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. <i>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. </i><b><i>— Mathematical Reviews</i></b> <i>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. </i><b><i>—Bulletin of the AMS </i></b> <i>The book is very well written and quite accessible; there is an excellent bibliography at the end. </i><b><i>—Zentralblatt MATH</i></b>
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Geometry and Spectra of Compact Riemann Surfaces (Modern Birkh�user Classics)
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Geometry and Spectra of Compact Riemann Surfaces (Modern Birkhäuser Classics)
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Paperback. Condizione: Very Good condition. NOT a library discard (illustratore). Reprint of the 1992 original. Boston: Birkhäuser, 2010. We have only this one copy, but it is available now and ready to ship today from Henderson, Nevada. Appears never read. Very Good condition. Bright, shiny, clean, square and tight. Flat, uncreased spine. Sharp corners. Mild creases to the front cover. Pages are fresh, crisp, clean and unmarked -- apparently never read. NO owner's name or bookplate. NOT a library discard. NOT a remainder. Appendix. Bibliography. Index. Bound in the original two-tone green wraps, lettered in white and dark green, with red decoration. From the publisher: "This 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. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.". Reprint of the 1992 original. Softcover. Very Good condition. Illus. by NOT a library discard. xvi, 456pp. Great Packaging, Fast Shipping. Codice articolo 031386
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Geometry and Spectra of Compact Riemann Surfaces.
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ISBN 10: 0817649913
ISBN 13: 9780817649913
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Paperback. Condizione: Very Good. Series: Modern Birkhäuser Classics. xvi 472p large format paperback, turquoise cover, like new condition, no noticeable wear, tight binding, clean and bright pages, all mathematical notation and diagrams very clear and sharp, an excellent copy with little to no sign of use Language: English Weight (g): 1460 Softcover reprint of hardcover edition 2010. Codice articolo 233053
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Geometry and Spectra of Compact Riemann Surfaces
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Geometry and Spectra of Compact Riemann Surfaces
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Springer Nature Singapore Nov 2010, 2010
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ISBN 13: 9780817649913
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 456 pp. Englisch. Codice articolo 9780817649913
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Geometry and Spectra of Compact Riemann Surfaces (Modern Birkhäuser Classics)
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Geometry and Spectra of Compact Riemann Surfaces (Modern Birkhäuser Classics)
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Taschenbuch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Codice articolo 9780817649913
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