发表机构
Beijing Normal University; Shanghai Institute for Mathematics and Interdisciplinary Sciences; Fudan University（北京师范大学; 上海数学与交叉学科研究院; 复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了数量曲率至少为6的完备非紧三维流形共轭半径至多2π/3，解决了Shen的猜想。
AI 中文摘要
我们证明，每个无边界、完备、连通且非紧的黎曼三维流形，若其数量曲率至少为 $6$，则其共轭半径至多为 $2\pi/3$。这解决了 Shen 关于三维中严格共轭半径界 $\operatorname{conj}(M,g)<\pi$ 的猜想。
英文摘要
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.
Comments9 pages
