Tohoku Mathematical Journal

On the $L^2$ form spectrum of the Laplacian on nonnegatively curved manifolds

Marco Rigoli and Alberto G. Setti

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Let $(M,g_o)$ be a complete, noncompact Riemannian manifold with a pole, and let $g=fg_o$ be a conformally related metric. We obtain conditions on the curvature of $g_o$ and on $f$ under which the Laplacian on $p$-forms on $(M,g)$ has no eigenvalues.

Article information

Tohoku Math. J. (2) Volume 53, Number 3 (2001), 443-452.

First available in Project Euclid: 3 May 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Differential forms Hodge Laplacian $L^2$-spectrum


Rigoli, Marco; Setti, Alberto G. On the $L^2$ form spectrum of the Laplacian on nonnegatively curved manifolds. Tohoku Math. J. (2) 53 (2001), no. 3, 443--452. doi:10.2748/tmj/1178207419.

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