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.
Original language | English (US) |
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Pages (from-to) | 1185-1210 |
Number of pages | 26 |
Journal | Journal of Geometric Analysis |
Volume | 25 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2015 |
Keywords
- Analytic surgery
- Hyperbolic cusps
- Hyperbolic funnels
- Inverse spectral problem
- Relatively isospectral
ASJC Scopus subject areas
- Geometry and Topology