Compactness of Relatively Isospectral Sets of Surfaces Via Conformal Surgeries

Pierre Albin; Clara L. Aldana; Frédéric Rochon

doi:10.1007/s12220-013-9463-0

Compactness of Relatively Isospectral Sets of Surfaces Via Conformal Surgeries

Pierre Albin, Clara L. Aldana, Frédéric Rochon

Mathematics

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	1185-1210
Number of pages	26
Journal	Journal of Geometric Analysis
Volume	25
Issue number	2
DOIs	https://doi.org/10.1007/s12220-013-9463-0
State	Published - Apr 2015

Keywords

Analytic surgery
Hyperbolic cusps
Hyperbolic funnels
Inverse spectral problem
Relatively isospectral

ASJC Scopus subject areas

Geometry and Topology

Online availability

10.1007/s12220-013-9463-0

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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.",

keywords = "Analytic surgery, Hyperbolic cusps, Hyperbolic funnels, Inverse spectral problem, Relatively isospectral",

author = "Pierre Albin and Aldana, {Clara L.} and Fr{\'e}d{\'e}ric Rochon",

note = "Funding Information: P. Albin was partially funded by NSF grant DMS-1104533. C.L. Aldana was partially funded by FCT project ptdc/mat/101007/2008. Registered at MPG, AEI-2012-059. F. Rochon was supported by grant DP120102019. Publisher Copyright: {\textcopyright} 2013, Mathematica Josephina, Inc.",

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language = "English (US)",

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AU - Albin, Pierre

AU - Aldana, Clara L.

AU - Rochon, Frédéric

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N2 - 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.

AB - 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.

KW - Analytic surgery

KW - Hyperbolic cusps

KW - Hyperbolic funnels

KW - Inverse spectral problem

KW - Relatively isospectral

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Compactness of Relatively Isospectral Sets of Surfaces Via Conformal Surgeries

Abstract

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