TY - JOUR
T1 - Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below
T2 - I
AU - Kondo, Kei
AU - Tanaka, Minoru
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/10
Y1 - 2011/10
N2 - 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 π. 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.
AB - 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 π. 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.
UR - http://www.scopus.com/inward/record.url?scp=80052737256&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80052737256&partnerID=8YFLogxK
U2 - 10.1007/s00208-010-0593-4
DO - 10.1007/s00208-010-0593-4
M3 - Article
AN - SCOPUS:80052737256
VL - 351
SP - 251
EP - 266
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 2
ER -