Conjugate radius of open manifolds

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 $λ_{0}(M)=0$ and scalar curvature $\ge n(n-1)$, then the conjugate radius $\le π$.