Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below (3)

DOI DOI DOI DOI DOI ほか6件をすべて表示 一部だけ表示 被引用文献7件 参考文献26件 オープンアクセス

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  • Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below, III
  • Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below: I
  • Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II

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This article is the third in a series of our investigation on a complete non-compact connected Riemannian manifold M. In the first series [KT1], we showed that all Busemann functions on an M which is not less curved than a von Mangoldt surface of revolution $¥widetilde{M}$ are exhaustions, if the total curvature of $¥widetilde{M}$ is greater than π. A von Mangoldt surface of revolution is, by definition, a complete surface of revolution homeomorphic to R2 whose Gaussian curvature is non-increasing along each meridian. Our purpose of this series is to generalize the main theorem in [KT1] to an M which is not less curved than a more general surface of revolution.

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