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arXiv · 2203.15211

Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions

Jiayin Pan·Guofang Wei
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Abstract

We give the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function at a point. This provides counterexamples to a longtime well-known open question whether the Busemann function at a point of an open manifold with nonnegative Ricci curvature is proper.

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Jiayin Pan, Guofang Wei. 2022-03-29. Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions. https://arxiv.org/abs/2203.15211

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