In this paper, we prove that if M is an open manifold with nonnegative Ricci curvature and large volume growth, positive critical radius, then sup Cp=∞.p∈M As an application, we give a theorem which supports strongly Petersen's conjecture.
This paper gives an estimate of excess functions of rays on complete noncompact manifolds.By using this estimation,the authors can get the results in [3] as corollaries,which asserts that a complete manifold is diffeomorphic to Rn under some curvature and pinching conditions.At last,they obtain a refinement of them with extra Ricci condition.
