%0 Journal Article
%T Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I
%A Kei Kondo
%A Minoru Tanaka
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s00208-010-0593-4
%X We investigate the finiteness structure of a complete non-compact $n$-dimensional Riemannian manifold $M$ whose radial curvature at a base point of $M$ is bounded from below by that of a non-compact von Mangoldt surface of revolution with its total curvature greater than $\pi$. We show, as our main theorem, that all Busemann functions on $M$ are exhaustions, and that there exists a compact subset of $M$ such that the compact set contains all critical points for any Busemann function on $M$. As corollaries by the main theorem, $M$ has finite topological type, and the isometry group of $M$ is compact.
%U http://arxiv.org/abs/0901.4010v2