Conjugate radius of open manifolds
classification
🧮 math.DG
keywords
boundconjugateradiuscurvatureopenscalarupperbottom-of-spectrum
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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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