  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.
