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Huber's Theorem for Hyperbolic Orbisurfaces

Published online by Cambridge University Press:  20 November 2018

Emily B. Dryden  and
Alexander Strohmaier
Emily B. Dryden
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, USA e-mail: ed012@bucknell.edu
Alexander Strohmaier
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK e-mail: A.Strohmaier@lboro.ac.uk
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Abstract

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We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. The converse also holds, giving a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces.

Keywords

58J5311F72Huber's theoremlength spectrumisospectralorbisurfaces

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 1 , 01 March 2009 , pp. 66 - 71
Copyright
Copyright © Canadian Mathematical Society 2009

References

[1] Doyle, P.G. and Rossetti, J.P., Isospectral hyperbolic surfaces have matching geodesics. http://arxiv.org/abs/math/0605765.Google Scholar
[2] Dryden, E.B., Geometric and Spectral Properties of Compact Riemann Orbisurfaces. Ph.D. Dissertation, Dartmouth College, Department of Mathematics, May 2004. http://www.facstaff.bucknell.edu/ed012/web thesis.pdf Google Scholar
[3] Dryden, E. B., Gordon, C. S., Greenwald, S. J., and Webb, D. L., Asymptotic expansion of the heat kernel for orbifolds. Michigan Math. J. 56(2008), no. 1, 205–238.Google Scholar
[4] Elstrodt, J., Grunewald, F., and Mennicke, J., Groups acting on hyperbolic space. Harmonic analysis and number theory. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998.Google Scholar
[5] Farsi, C., Orbifold spectral theory. Rocky Mountain J. Math. 31(2001), no. 1, 215–235.Google Scholar
[6] Guillopé, L. and Zworski, M., The wave trace for Riemann surfaces. Geom. Funct. Anal. 9(1999), no. 6, 1156–1168.Google Scholar
[7] Hejhal, D. A., The Selberg trace formula for PSL(2, R) Vol. I. Lecture Notes inMathematics 548, Springer-Verlag, Berlin, 1976.Google Scholar
[8] Iwaniec, H., Spectral methods of automorphic forms. Graduate Studies in Mathematics 53, American Mathematical Society, Providence, RI, 2002.Google Scholar
[9] Parnovskiĭ, L. B., The Selberg trace formula and the Selberg zeta function for cocompact discrete subgroup SO+(1, n). Funktsional. Anal. i Prilozhen. 26(1992), no. 3, 55–64.Google Scholar
[10] Shams, N., Stanhope, E., and Webb, D. L., One cannot hear orbifold isotropy type. Arch. Math., 87(2006), no. 4, 375–384.Google Scholar
[11] Stanhope, E., Spectral bounds on orbifold isotropy. Ann. Global Anal. Geom. 27(2005), no. 4, 355–375.Google Scholar
[12] Thurston, W. P., The Geometry and Topology of Three-Manifolds, Electronic edition of 1980 lecture notes distributed by Princeton University, http://www.msri.org/publications/books/gt3m/.Google Scholar