Abstract.
Let M be a complete open n-manifold with a base point p, at which the radial sectional curvature along every minimizing geodesic emanating from p is bounded below by the radial curvature function of a model surface. We discuss the maximal diameter theorem for the compactification of M by attaching the ideal boundary. Under certain conditions we prove that p becomes a pole and that M is isometric to the n-model.
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Received: 24 September 2000; in final form: 21 November 2001 / Published online: 17 June 2002
Dedicated to Professor Su Bu-Chin on the occasion of his one hundredth birthday
The work of the first author was partially supported by the Grant-in-Aid for Scientific Research, No. 12440021 and for Exploratory Research, No. 13874012
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Shiohama, K., Tanaka, M. Compactification and maximal diameter theorem for noncompact manifolds with radial curvature bounded below. Math Z 241, 341–351 (2002). https://doi.org/10.1007/s002090200418
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DOI: https://doi.org/10.1007/s002090200418