Abstract
We show that certain families of iso-length spectral hyperbolic surfaces obtained via the Sunada construction are not generally simple iso-length spectral.
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Abikoff W.: The Real Analytic Theory of Teichmüller Space, vol. 820 of Lecture Notes in Mathematics. Springer, Berlin (1980)
Brooks R., Tse R.: Isospectral surfaces of small genus. Nagoya Math. J. 107, 13–24 (1987)
Buser P.: Isospectral Riemann surfaces. Ann. Inst. Fourier (Grenoble) 36(2), 167–192 (1986)
Buser P.: Geometry and Spectra of Compact Riemann Surfaces volume 106 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA (1992)
Kerckhoff S.: Earthquakes are analytic. Comment. Math. Helvetici 60, 17–30 (1985). doi:10.1007/BF02567397
Leininger, C.J., McReynolds, D.B., Neumann, W.D., Reid, A.W.: Length and eigenvalue equivalence. Int. Math. Res. Not. IMRN 135(24), (2007)
Leininger C. J.: Equivalent curves in surfaces. Geom. Dedicata 102, 151–177 (2003)
McShane G., Parlier H.: Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space. Geom. Topol. 12(4), 1883–1919 (2008)
Randol B.: The length spectrum of a Riemann surface is always of unbounded multiplicity. Proc. Am. Math. Soc. 78(3), 455–456 (1980)
Sunada T.: Riemannian coverings and isospectral manifolds. Ann. Math. 121(1), 169–186 (1985)
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Maungchang, R. The Sunada construction and the simple length spectrum. Geom Dedicata 163, 349–360 (2013). https://doi.org/10.1007/s10711-012-9753-x
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DOI: https://doi.org/10.1007/s10711-012-9753-x