Abstract
Let M be a complete non-compact connected Riemannian n-dimensional manifold. We first prove that, for any fixed point pεM, the radial Ricci curvature of M at p is bounded from below by the radial curvature function of some non-compact n-dimensional model. Moreover, we then prove, without the pointed Gromov-Hausdorff convergence theory, that, if model volume growth is sufficiently close to 1, then M is diffeomorphic to Euclidean n-dimensional space. Hence, our main theorem has various advantages of the Cheeger-Colding diffeomorphism theorem via the Euclidean volume growth. Our main theorem also contains a result of do Carmo and Changyu as a special case.
Original language | English |
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Pages (from-to) | 597-605 |
Number of pages | 9 |
Journal | Differential Geometry and its Application |
Volume | 29 |
Issue number | 4 |
DOIs | |
Publication status | Published - Aug 2011 |
Externally published | Yes |
Keywords
- Radial curvature
- Ricci curvature
- Volume growth
ASJC Scopus subject areas
- Analysis
- Geometry and Topology
- Computational Theory and Mathematics