A refinement of strong multiplicity one for spectra of hyperbolic manifolds

Details A refinement of strong multiplicity one for spectra of hyperbolic manifolds A refinement of strong multiplicity one for spectra of hyperbolic manifolds

2011-08-15

arxiv.org/abs/1108.2977v2

Mathematics

Spectral Theory

45 pages, added references, added last subsection

Scientific paper

Let $\calM_1$ and $\calM_2$ denote two compact hyperbolic manifolds. Assume that the multiplicities of eigenvalues of the Laplacian acting on $L^2(\calM_1)$ and $L^2(\calM_2)$ (respectively, multiplicities of lengths of closed geodesics in $\calM_1$ and $\calM_2$) are the same, except for a possibly infinite exceptional set of eigenvalues (respectively lengths). We define a notion of density for the exceptional set and show that if it is below a certain threshold, the two manifolds must be iso-spectral.

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