Electrostatic inequalities and stability of matter on asymptotically Euclidean manifolds

We prove stability of nonrelativistic fermionic matter in the presence of fixed nuclei $\{R_j\}$ on an asymptotically Euclidean Riemannian manifold $(M,g)$. Upper and lower bounds on sectional curvatures are assumed, but no specific sign conditions on the curvature are imposed. The proof follows the route of Lieb-Thirring and electrostatic inequalities, the latter being proved by means of a Voronoi decomposition type argument which is however based on the Green functions $\{G(\cdot ,R_j)\}$ rather than the distance function.