Manifolds tightly covered by two metric balls

Jianming Wan

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arXiv · 1610.08190

Manifolds tightly covered by two metric balls

Jianming Wan

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Abstract

In this note we provide natural optimal geometric conditions for a Riemannian manifold suitably covered by two open metric balls to be homeomorphic to a sphere. This can be viewed as a geometric analogue of Brown's theorem in topology stating that a closed manifold covered by two topological balls is a sphere.

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Jianming Wan. 2016-10-26. Manifolds tightly covered by two metric balls. https://arxiv.org/abs/1610.08190

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