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Rays and souls in von
Mangoldt planes
Igor Belegradek, Eric Choi and Nobuhiro Innami |
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Vol. 259 (2012), No. 2, 279–306
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Abstract |
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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 ℝ3 can be smoothed to a von Mangoldt plane. |
Keywords
radial curvature, critical point, von Mangoldt, surface of
revolution, ray, nonnegative curvature, soul
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Mathematical Subject Classification 2010
Primary: 53C20, 53C22, 53C45
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Milestones
Received: 14 November 2011
Revised: 5 June 2012
Accepted: 8 June 2012
Published: 3 October 2012
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Authors |
| Igor Belegradek | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160 United States |
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| Eric Choi | |
| Department of Mathematics and
Computer Science Emory University 400 Dowman Dr., W401 Atlanta, GA 30322 United States |
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| Nobuhiro Innami | |
| Department of Mathematics Faculty of Science Niigata University Niigata 950-2181 Japan |
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