Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces

Kei Kondo, Minoru Tanaka

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)597-605
Number of pages9
JournalDifferential Geometry and its Application
Issue number4
Publication statusPublished - Aug 2011
Externally publishedYes


  • Radial curvature
  • Ricci curvature
  • Volume growth

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics


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