Electrostatic inequalities and stability of matter on asymptotically Euclidean manifolds

Abstract

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.