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Spectral Geometry of the Steklov Problem on Orbifolds

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Spectral Geometry of the Steklov Problem on Orbifolds. / Hassannezhad, Asma; Arias-Marco, Teresa; Dryden, Emily; Gordon, Carolyn; Ray, Allie; Stanhope, Elizabeth.

In: International Mathematics Research Notices, Vol. 2019, No. 1, rnx117, 01.2019, p. 90-139.

Research output: Contribution to journalArticle

Harvard

Hassannezhad, A, Arias-Marco, T, Dryden, E, Gordon, C, Ray, A & Stanhope, E 2019, 'Spectral Geometry of the Steklov Problem on Orbifolds', International Mathematics Research Notices, vol. 2019, no. 1, rnx117, pp. 90-139. https://doi.org/10.1093/imrn/rnx117

APA

Hassannezhad, A., Arias-Marco, T., Dryden, E., Gordon, C., Ray, A., & Stanhope, E. (2019). Spectral Geometry of the Steklov Problem on Orbifolds. International Mathematics Research Notices, 2019(1), 90-139. [rnx117]. https://doi.org/10.1093/imrn/rnx117

Vancouver

Hassannezhad A, Arias-Marco T, Dryden E, Gordon C, Ray A, Stanhope E. Spectral Geometry of the Steklov Problem on Orbifolds. International Mathematics Research Notices. 2019 Jan;2019(1):90-139. rnx117. https://doi.org/10.1093/imrn/rnx117

Author

Hassannezhad, Asma ; Arias-Marco, Teresa ; Dryden, Emily ; Gordon, Carolyn ; Ray, Allie ; Stanhope, Elizabeth. / Spectral Geometry of the Steklov Problem on Orbifolds. In: International Mathematics Research Notices. 2019 ; Vol. 2019, No. 1. pp. 90-139.

Bibtex

@article{29528a9b312b4e81ac60f5ba45cf566e,
title = "Spectral Geometry of the Steklov Problem on Orbifolds",
abstract = "We consider how the geometry and topology of a compact $n$-dimensional Riemannian orbifold with boundary relates to its Steklov spectrum. In two dimensions, motivated by work of A. Girouard, L. Parnovski, I. Polterovich, and D. Sher in the manifold setting, we compute the precise asymptotics of the Steklov spectrum in terms of only boundary data. As a consequence, we prove that the Steklov spectrum detects the presence and number of orbifold singularities on the boundary of an orbisurface and it detects the number each of smooth and singular boundary components. Moreover, we find that the Steklov spectrum also determines the lengths of the boundary components modulo an equivalence relation, and we show by examples that this result is the best possible. We construct various examples of Steklov isospectral Riemannian orbifolds which demonstrate that these two-dimensional results do not extend to higher dimensions.",
author = "Asma Hassannezhad and Teresa Arias-Marco and Emily Dryden and Carolyn Gordon and Allie Ray and Elizabeth Stanhope",
year = "2019",
month = "1",
doi = "10.1093/imrn/rnx117",
language = "English",
volume = "2019",
pages = "90--139",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "1",

}

RIS - suitable for import to EndNote

TY - JOUR

T1 - Spectral Geometry of the Steklov Problem on Orbifolds

AU - Hassannezhad, Asma

AU - Arias-Marco, Teresa

AU - Dryden, Emily

AU - Gordon, Carolyn

AU - Ray, Allie

AU - Stanhope, Elizabeth

PY - 2019/1

Y1 - 2019/1

N2 - We consider how the geometry and topology of a compact $n$-dimensional Riemannian orbifold with boundary relates to its Steklov spectrum. In two dimensions, motivated by work of A. Girouard, L. Parnovski, I. Polterovich, and D. Sher in the manifold setting, we compute the precise asymptotics of the Steklov spectrum in terms of only boundary data. As a consequence, we prove that the Steklov spectrum detects the presence and number of orbifold singularities on the boundary of an orbisurface and it detects the number each of smooth and singular boundary components. Moreover, we find that the Steklov spectrum also determines the lengths of the boundary components modulo an equivalence relation, and we show by examples that this result is the best possible. We construct various examples of Steklov isospectral Riemannian orbifolds which demonstrate that these two-dimensional results do not extend to higher dimensions.

AB - We consider how the geometry and topology of a compact $n$-dimensional Riemannian orbifold with boundary relates to its Steklov spectrum. In two dimensions, motivated by work of A. Girouard, L. Parnovski, I. Polterovich, and D. Sher in the manifold setting, we compute the precise asymptotics of the Steklov spectrum in terms of only boundary data. As a consequence, we prove that the Steklov spectrum detects the presence and number of orbifold singularities on the boundary of an orbisurface and it detects the number each of smooth and singular boundary components. Moreover, we find that the Steklov spectrum also determines the lengths of the boundary components modulo an equivalence relation, and we show by examples that this result is the best possible. We construct various examples of Steklov isospectral Riemannian orbifolds which demonstrate that these two-dimensional results do not extend to higher dimensions.

UR - https://arxiv.org/abs/1609.05142

U2 - 10.1093/imrn/rnx117

DO - 10.1093/imrn/rnx117

M3 - Article

VL - 2019

SP - 90

EP - 139

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 1

M1 - rnx117

ER -