Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces

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