Eigenfunctions of the Laplacian on rotationally symmetric manifolds

Marias, Michel

doi:10.1090/S0002-9947-98-02354-X

Eigenfunctions of the Laplacian on rotationally symmetric manifolds
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Trans. Amer. Math. Soc. 350 (1998), 4367-4375 Request permission

Abstract:

Eigenfunctions of the Laplacian on a negatively curved, rotationally symmetric manifold $M=(\mathbf {R}^n,ds^2),$ $ds^2=dr^2+f(r)^2d\theta ^2,$ are constructed explicitly under the assumption that an integral of $f(r)$ converges. This integral is the same one which gives the existence of nonconstant harmonic functions on $M.$

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