Resolvent of the Laplacian on geometrically finite hyperbolic manifolds
Resolvent of the Laplacian on geometrically finite hyperbolic manifolds
复制标题
几何有限双曲流形上拉普拉斯算子的求解
作者：
C. Guillarmou;R. Mazzeo
对于几何有限双曲流形Γ n+1，证明了Laplacian、Poincaré级数、Einsenstein级数和散射算子的预解式在整个复平面上的亚纯扩张.我们还根据Γ的极限集的Hausdorff维数，导出了Γ在n+1大球上的格点的渐近性.
For geometrically finite hyperbolic manifolds Γℍn+1, we prove the meromorphic extension of the resolvent of Laplacian, Poincaré series, Einsenstein series and scattering operator to the whole complex plane. We also deduce the asymptotics of lattice points of Γ in large balls of ℍn+1 in terms of the Hausdorff dimension of the limit set of Γ.