Consider H_m × H_n the Cartesian product of two hyperbolic spaces with dimensions m and n respectively. It carries the product Riemannian structure and corresponding Laplace-Beltrami operator Δ=Δ_m x Δ_n, the sum of the Laplace Beltrami operators on the two factors. It is well known that there exist positive functions h on H_m × H_n which satisfy Δh=λh if and only if λ≥λ_0, where λ_0=-((m-1)/2)^2-((n-1)/2)^2 is the bottom of the positive spectrum.
The Martin compactification of the Cartesian product of two hyperbolic spaces
GIULINI, SAVERIO;
1993-01-01
Abstract
Consider H_m × H_n the Cartesian product of two hyperbolic spaces with dimensions m and n respectively. It carries the product Riemannian structure and corresponding Laplace-Beltrami operator Δ=Δ_m x Δ_n, the sum of the Laplace Beltrami operators on the two factors. It is well known that there exist positive functions h on H_m × H_n which satisfy Δh=λh if and only if λ≥λ_0, where λ_0=-((m-1)/2)^2-((n-1)/2)^2 is the bottom of the positive spectrum.
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