A Bonnet-Myers Theorem from a spectral assumption

We obtain a finiteness result for the fundamental group of a closed Riemannian manifold $(M^n,g)$ under the assumption that the Schrödinger operator $\Delta_g+(n-2)/\rho$ is positive (where at $x\in M$, $\rho(x)$ is the lowest eigenvalue of the Ricci tensor at $x$). It is a joint work with C. Rose (MPI Leipzig).