Mathematics – Differential Geometry
Scientific paper
2009-01-26
Trans. Amer. Math. Soc. 362 (2010), 6293-6324
Mathematics
Differential Geometry
37 pages, No figures, Submitted to Transactions of Amer. Math. Soc. (December 17, 2007), The [v1] is the 2nd revised version (
Scientific paper
We prove, as our main theorem, the finiteness of topological type of a complete open Riemannian manifold $M$ with a base point $p \in M$ whose radial curvature at $p$ is bounded from below by that of a non-compact model surface of revolution $\tilde{M}$ which admits a finite total curvature and has no pair of cut points in a sector. Here a sector is, by definition, a domain cut off by two meridians emanating from the base point $\tilde{p} \in \tilde{M}$. Notice that our model $\tilde{M}$ does not always satisfy the diameter growth condition introduced by Abresch and Gromoll. In order to prove the main theorem, we need a new type of the Toponogov comparison theorem. As an application of the main theorem, we present a partial answer to Milnor's open conjecture on the fundamental group of complete open manifolds.
Kondo Kei
Tanaka Minoru
No associations
LandOfFree
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-372138