We prove that the asymptotic cone of every complete, connected, non-compact Riemannian manifold of roughly non-negative radial curvature exists, and it is isometric to the Euclidean cone over their Tits ideal boundaries.
@article{1160745813,
author = {MASHIKO, Yukihiro and NAGANO, Koichi and OTSUKA, Kazuo},
title = {The asymptotic cones of manifolds of roughly non-negative radial curvature},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 55-68},
language = {en},
url = {http://dml.mathdoc.fr/item/1160745813}
}
MASHIKO, Yukihiro; NAGANO, Koichi; OTSUKA, Kazuo. The asymptotic cones of manifolds of roughly non-negative radial curvature. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 55-68. http://gdmltest.u-ga.fr/item/1160745813/