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arXiv · 2610.09773

A conjugate radius bound for open three-manifolds

Jian Ge·Chuanhuan Li
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Abstract

We prove that every complete, connected, noncompact Riemannian three-manifold without boundary with scalar curvature at least $6$ has conjugate radius at most $2π/3$. This resolves Shen's conjecture on the strict conjugate-radius bound $\operatorname{conj}(M,g)<π$ in dimension three.

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Jian Ge, Chuanhuan Li. 2026-10-07. A conjugate radius bound for open three-manifolds. https://arxiv.org/abs/2610.09773

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