Rays and souls in von Mangoldt planes

Details Rays and souls in von Mangoldt planes Rays and souls in von Mangoldt planes

2011-08-06

arxiv.org/abs/1108.1515v1

Mathematics

Differential Geometry

24 pages

Scientific paper

We study rays and critical points of Busemann functions in von Mangoldt
planes, which has applications to the structure of open complete manifolds with
lower radial curvature bounds. We compute the set of souls for every von
Mangoldt plane of nonnegative curvature. We show that each cone in the
Euclidean 3-space can be smoothed to a von Mangoldt plane.

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