Abstract: We present a splitting theorem for Riemannian manifolds that satisfy a spectral notion of nonnegative lower bound on the Ricci curvature. More precisely, such a lower bound is encoded in the fact that the spectrum of a suitable Schrodinger operator that involves the least eigenvalue of the Ricci tensor is nonnegative. We prove that if a manifold has multiple ends and nonnegative Ricci curvature in the spectral sense, then it has nonnegative Ricci curvature in the pointwise classical sense and then it splits isometrically. We will also discuss the sharpness of our assumptions. The result provides a sharp spectral generalization of the celebrated Cheeger-Gromoll splitting theorem in the case of multiple ends. The talk is based on a joint work in collaboration with Gioacchino Antonelli (University of Notre Dame) and Kai Xu (UC Berkeley).

For further information please contact elisur.magrini@unibocconi.it