A lower bound for the $\Theta$ function on manifolds without conjugate   points
  In this short note, we prove that the usual $\Theta$ function on a Riemannian manifold without conjugate points is uniformly bounded from below. This extends a result of Green in two dimensions. This elementary lemma implies that the B\'erard remainder in the Weyl law is valid for a manifold without conjugate points, without any restriction on the dimension. 
Yannick Bonthonneau
math.DG math.SP