A lower bound for the spectrum of the Laplacian in terms of sectional and Ricci curvature

Setti, Alberto G.

doi:10.1090/S0002-9939-1991-1043421-3

A lower bound for the spectrum of the Laplacian in terms of sectional and Ricci curvature
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by Alberto G. Setti PDF

Proc. Amer. Math. Soc. 112 (1991), 277-282 Request permission

Abstract:

Let $M$ be an $n$-dimensional, complete, simply connected Riemannian manifold. In this paper we show that if the sectional curvature is bounded above by $- k \leq 0$ and the Ricci curvature is bounded above by $- \alpha \leq 0$, then the spectrum of the Laplacian on $M$ is bounded below by $[\alpha + (n - 1)(n - 2)k]/4$. This improves a previous result due to H. P. McKean.

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