We show that for an arbitrarily given closed Riemannian manifold M admitting a point p ∊ M with a single cut point, every closed Riemannian manifold N admitting a point q ∊ N with a single cut point is diffeomorphic to M if the radial curvatures of N at q are sufficiently close in the sense of L1-norm to those of M at p.
- Bi-Lipschitz homeomorphism
- Differentiable sphere theorem
- Exotic spheres
- Radial curvature
- The Blaschke conjecture for spheres
- The Cartan-Ambrose-Hicks theorem
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