Geodesic
Huber's Theorem for Hyperbolic Orbisurfaces
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 66-71

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2009-008-0
Mots-clés : 58J53, 11F72, Huber's theorem, length spectrum, isospectral, orbisurfaces 
Dryden, Emily B.; Strohmaier, Alexander. Huber's Theorem for Hyperbolic Orbisurfaces. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 66-71. doi: 10.4153/CMB-2009-008-0
@article{10_4153_CMB_2009_008_0,
     author = {Dryden, Emily B. and Strohmaier, Alexander},
     title = {Huber's {Theorem} for {Hyperbolic} {Orbisurfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {66--71},
     year = {2009},
     volume = {52},
     number = {1},
     doi = {10.4153/CMB-2009-008-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-008-0/}
}
TY  - JOUR
AU  - Dryden, Emily B.
AU  - Strohmaier, Alexander
TI  - Huber's Theorem for Hyperbolic Orbisurfaces
JO  - Canadian mathematical bulletin
PY  - 2009
SP  - 66
EP  - 71
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-008-0/
DO  - 10.4153/CMB-2009-008-0
ID  - 10_4153_CMB_2009_008_0
ER  - 
%0 Journal Article
%A Dryden, Emily B.
%A Strohmaier, Alexander
%T Huber's Theorem for Hyperbolic Orbisurfaces
%J Canadian mathematical bulletin
%D 2009
%P 66-71
%V 52
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-008-0/
%R 10.4153/CMB-2009-008-0
%F 10_4153_CMB_2009_008_0

[1] [1] Doyle, P.G. and Rossetti, J.P., Isospectral hyperbolic surfaces have matching geodesics. . Google Scholar | arXiv

[2] [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] [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] [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] [5] Farsi, C., Orbifold spectral theory. Rocky Mountain J. Math. 31(2001), no. 1, 215–235. Google Scholar

[6] [6] Guillopé, L. and Zworski, M., The wave trace for Riemann surfaces. Geom. Funct. Anal. 9(1999), no. 6, 1156–1168. Google Scholar

[7] [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] [8] Iwaniec, H., Spectral methods of automorphic forms. Graduate Studies in Mathematics 53, American Mathematical Society, Providence, RI, 2002. Google Scholar

[9] [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] [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] [11] Stanhope, E., Spectral bounds on orbifold isotropy. Ann. Global Anal. Geom. 27(2005), no. 4, 355–375. Google Scholar

[12] [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

Cité par Sources :