Conjugate radius of open manifolds

Jian Ge; Shimeng Zhang

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arXiv · 2605.28379

Conjugate radius of open manifolds

Jian Ge·Shimeng Zhang

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Abstract

In this short note, we establish an upper bound for the conjugate radius of an open $n$-dimensional Riemannian manifold under a scalar curvature lower bound and a bottom-of-spectrum upper bound. As a consequence, if $\lambda_{0}(M)=0$ and scalar curvature $\ge n(n-1)$, then the conjugate radius $\le \pi$.

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Jian Ge, Shimeng Zhang. 2026-05-27. Conjugate radius of open manifolds. https://arxiv.org/abs/2605.28379

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