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Spectral Theory of Infinite-Area Hyperbolic Surfaces pp 297–318Cite as

Birkhäuser

Inverse Spectral Geometry

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Part of the book series: Progress in Mathematics ((PM,volume 318))

Abstract

Determining the spectral properties of the Laplacian on a given Riemannian manifold is a “forward” spectral problem. The corresponding “inverse” problem is to deduce geometric properties from some knowledge of the spectrum. In the case of a surface with hyperbolic ends, the input data could include the resonance set, the scattering phase, perhaps even the scattering matrix for a particular set of frequencies.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, USA

    David Borthwick

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  1. David Borthwick
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Borthwick, D. (2016). Inverse Spectral Geometry. In: Spectral Theory of Infinite-Area Hyperbolic Surfaces. Progress in Mathematics, vol 318. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-33877-4_13

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