Description:
<jats:p>It is demonstrated, via recent global estimates for the heat kernel found by Li and Yau [Acta Matematica 156, 153 (1986)], that the covariance of the mass m free field decays exponentially, at a rate m, with the geodesic distance on any complete, noncompact Riemannian manifold with non-negative Ricci curvature. The rate of the exponential decay is larger than m on simply connected manifolds with negative sectional curvature.</jats:p>