  We show that the ground state energy is bounded from below when there are
infinitely many attractive delta function potentials placed in arbitrary
locations, while all being separated at least by a minimum distance, on two
dimensional non-compact manifold. To facilitate the reading of the paper, we
first present the arguments in the setting of Cartan-Hadamard manifolds and
then subsequently discuss the general case. For this purpose, we employ the
heat kernel techniques as well as some comparison theorems of Riemannian
geometry, thus generalizing the arguments in the flat case following the
approach presented in Albeverio et. al. (2004).
