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arXiv · 1004.3826

Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces

Kei Kondo·Minoru Tanaka
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Abstract

Let M be a complete non-compact connected Riemannian n-dimensional manifold. We first prove that, for any fixed point p in M, 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.

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Kei Kondo, Minoru Tanaka. 2011-05-19. Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces. https://doi.org/10.1016/j.difgeo.2011.04.040

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