On the spectrum of a finite-volume negatively-curved manifold

Details On the spectrum of a finite-volume negatively-curved manifold On the spectrum of a finite-volume negatively-curved manifold

1999-08-26

arxiv.org/abs/math/9908136v2

Mathematics

Differential Geometry

17 pages, statement of Theorem 2 improved

Scientific paper

We show that a noncompact manifold with bounded sectional curvature, whose ends are sufficiently Gromov-Hausdorff close to rays, has a finite dimensional space of square-integrable harmonic forms. In the special case of a finite-volume manifold with pinched negative sectional curvature, we show that the essential spectrum of the p-form Laplacian is the union of the essential spectra of a collection of ordinary differential operators associated to the ends. We give examples of such manifolds with curvature pinched arbitrarily close to -1 and with an infinite number of gaps in the spectrum of the function Laplacian.

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