RAYS AND SOULS IN VON MANGOLDT PLANES

摘要

We study rays in von Mangoldt planes, which has applications to the structure of open complete manifolds with lower radial curvature bounds. We prove that the set of souls of any rotationally symmetric plane of nonnega-tive curvature is a closed ball, and if the plane is von Mangoldt we compute the radius of the ball. We show that each cone in ?3 can be smoothed to a von Mangoldt plane.