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arXiv · 2504.05459

Length of a closed geodesic in 3-manifolds of positive scalar curvature

Yevgeny Liokumovich·Davi Maximo·Regina Rotman
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Abstract

Let $M$ be a closed $3$-dimensional Riemannian manifold with positive scalar curvature, $R_g \geq 6$. We show that $M$ contains a non-trivial closed geodesic of length less than $22500$. This confirms a conjecture of M. Gromov in dimension $3$.

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Yevgeny Liokumovich, Davi Maximo, Regina Rotman. 2025-04-07. Length of a closed geodesic in 3-manifolds of positive scalar curvature. https://arxiv.org/abs/2504.05459

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