Paper detail

Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. III

Dedicated to Professor K. Shiohama on the occasion of his seventieth birthday: This article is the third in a series of our investigation on a complete non-compact connected Riemannian manifold $M$. In the first series [arXiv:0901.4010], we showed that all Busemann functions on an $M$ which is not less curved than a von Mangoldt surface of revolution are exhaustions, if the total curvature of the surface is greater than $π$. A von Mangoldt surface of revolution is, by definition, a complete surface of revolution homeomorphic to Euclidean plane whose Gaussian curvature is non-increasing along each meridian. Our purpose of this series is to generalize the main theorem in [arXiv:0901.4010] to an $M$ which is not less curved than a more general surface of revolution.