Rays and souls in von Mangoldt planes
arXiv:1108.1515
Abstract
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 nonnegative 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 the Euclidean 3-space can be smoothed to a von Mangoldt plane.
arXiv comment28 pages