Tohoku Mathematical Journal
2001
September
SECOND SERIES VOL. 53, NO. 3

Tohoku Math. J.
53 (2001), 443-452

Title ON THE $L^{2}$ FORM SPECTRUM OF THE LAPLACIAN ON NONNEGATIVELY CURVED MANIFOLDS

Author Marco Rigoli and Alberto G. Setti

(Received September 29, 1999, revised August 3, 2000)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 58A10, 58G25.
Key words and phrases. Differential forms, Hodge Laplacian, $L^2$-spectrum.

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