Collapsing manifolds with boundary |
| |
Authors: | Jeremy Wong |
| |
Institution: | (1) Department of Mathematics, University of Illinois, 1409 W. Green St, Urbana, IL 61801, U.S.A |
| |
Abstract: | This paper studies manifolds-with-boundary collapsing in the Gromov– Hausdorff topology. The main aim is an understanding
of the relationship of the topology and geometry of a limiting sequence of manifolds-with-boundary to that of a limit space,
which is presumed to be without geodesic terminals. The first group of results provide a fiber bundle structure to the manifolds-with-boundary.
One of the main theorems establishes a disc bundle structure for any manifold-with-boundary having two-sided bounds on sectional
curvature and second fundamental form, and a lower bound on intrinsic injectivity radius, which is sufficiently close in the
Gromov–Hausdorff topology to a closed manifold. Another result is a rough version of Toponogov’s Splitting Theorem. The second
group of results identify Gromov–Hausdorff limits of certain sequences of manifolds with non-convex boundaries as Alexandrov
spaces of curvature bounded below. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|