A lower bound for the least eigenvalue of \(\Delta +V\) (Q2638633)

Let \(M^ n\) be a closed n dimensional Riemannian manifold, let \(\Delta\) be the scalar Laplacian, and let V: \(M\to {\mathbb{R}}\) be continuous. The author gives a sufficient condition for \(\Delta +V\) to be positive in terms of geometric assumptions on M; the author also gives an application to a Bochner type vanishing theorem.