In this paper we prove that for every complete n-dimensional Riemannian manifold without Green's function and with its sectional curvatures satisfying Kâ¤â1, the exponent of convergence is greater than or equal to nâ1. Furthermore, we show that this inequality is sharp. This result is well known for manifolds with constant sectional curvatures K=â1.
Classification
subjects
Mathematics
keywords
riemannian manifold; negative curvature; greens function; first eigenvalue; exponent of convergence