A Lower Bound for the Spectrum of the Laplacian in Terms of Sectional and Ricci Curvature
A Lower Bound for the Spectrum of the Laplacian in Terms of Sectional and Ricci Curvature
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 …