Geometry and Spectra of Compact Riemann Surfaces

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Focusing on the geometric theory of compact Riemann surfaces with genus greater than one, the book explores the Laplace operator's relationship to this geometry. Originating from a thesis on Bers' pants decomposition theorem, it incorporates innovative cutting and pasting techniques related to hyperbolic geodesic polygons. The author expands on this foundation, integrating recent advancements in the field, including Sunada's isospectral manifolds. The text features new proofs and previously unpublished results, reflecting the evolving nature of the subject.