Spectral Theory of Infinite-Area Hyperbolic Surfaces
Description
This book is a self-contained monograph on spectral theory for non-compact Riemann surfaces, focused on the infinite-volume case. By focusing on the scattering theory of hyperbolic surfaces, this work provides a compelling introductory example which will be accessible to a broad audience. The book opens with an introduction to the geometry of hyperbolic surfaces. Then a thorough development of the spectral theory of a geometrically finite hyperbolic surface of infinite volume is given. The final sections include recent developments for which no thorough account exists.
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From the reviews:
"The core of the book under review is devoted to the detailed description of the Guillopé-Zworski papers . . The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed . . The book gathers together some material which is not always easily available in the literature . . To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader . would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)
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