A refinement of strong multiplicity one for spectra of hyperbolic manifolds
A refinement of strong multiplicity one for spectra of hyperbolic manifolds
复制标题
双曲流形谱强重数的一种细化
DOI：
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发表时间：
2011
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通讯作者：
Dubi Kelmer
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作者：
Dubi Kelmer
设$\Calm_1$和$\Calm_2$表示两个紧致双曲流形。假设作用于$L^2(\Calm_1)$和$L^2(\Calm_2)$(分别为$\Calm_1$和$\Calm_2$中的闭测地线的长度的重数)上的拉普拉斯本征值的重数是相同的，除了可能有无限个例外的特征值集(分别是长度)。我们定义了例外集的密度的概念，并证明了如果它低于某个阈值，则两个流形一定是等谱的。
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.