论文信息 - On the least positive eigenvalue of the Laplacian for the compact quotient of a certain Riemannian symmetric space

On the least positive eigenvalue of the Laplacian for the compact quotient of a certain Riemannian symmetric space

Let (M, g) be the standard Euclidean space or a Riemannian symmetric space of non-compact type of rank one. Let G be the identity component of the Lie group of all isometries of (M, g). Let Γ be a discrete subgroup of G acting fixed point freely on M whose quotient manifold MΓ is compact. Let — ΔΓ be the Laplace-Beltrami operator (cf. [4]) acting on smooth functions on MΓ for the Riemannian metric gΓ on MΓ induced by g. The compactness of MΓ implies that the spectrum of ΔΓ forms a discrete subset of the set of non-negative real numbers. Let λx(Γ) be the least positive eigenvalue of ΔΓ. Let vol (MΓ) be the volume of (MΓ, gΓ). Then we have

Hajime Urakawa

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