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

John Lott

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arXiv · math/9908136

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

John Lott

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Abstract

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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John Lott. 2000-09-10. On the spectrum of a finite-volume negatively-curved manifold. https://arxiv.org/abs/math/9908136

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