Answers are grounded in this paper and cite their sources.
New examples demonstrate the existence of non-proper Busemann functions in open manifolds with positive Ricci curvature, suggesting potential implications for geometry.
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 the longtime well-known open question of whether the Busemann function at a point of an open manifold with nonnegative Ricci curvature is proper.
No takes yet. Share an insight, caveat, or question.
Pan et al. (2026) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: