Compactness of relatively isospectral sets of surfaces via conformal surgeries

Albin, Pierre; Aldana, Clara Lucia; Rochon, Frédéric

doi:10.1007/s12220-013-9463-0

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Compactness of relatively isospectral sets of surfaces via conformal surgeries

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Aldana, Clara Lucia
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1206.6077
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JGA25_1185.pdf
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Citation

Albin, P., Aldana, C. L., & Rochon, F. (2015). Compactness of relatively isospectral sets of surfaces via conformal surgeries. Journal of Geometric Analysis, 25(2), 1185-1210. doi:10.1007/s12220-013-9463-0.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-A8A0-B

Abstract

We introduce a notion of relative isospectrality for surfaces with boundary having possibly non-compact ends either conformally compact or asymptotic to cusps. We obtain a compactness result for such families via a conformal surgery that allows us to reduce to the case of surfaces hyperbolic near infinity recently studied by Borthwick and Perry, or to the closed case by Osgood, Phillips and Sarnak if there are only cusps.