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arXiv · 2412.02028

Besicovitch-type inequality for closed geodesics on 2-dimensional spheres

Talant Talipov
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Abstract

We prove the existence of a constant $C > 0$ such that for any Riemannian metric $g$ on a 2-dimensional sphere $S^2$, there exist two distinct closed geodesics with lengths $L_{1}$ and $L_{2}$ satisfying $L_{1} L_{2} \leq C \cdot \operatorname{Area}(S^2, g)$.

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Talant Talipov. 2024-12-02. Besicovitch-type inequality for closed geodesics on 2-dimensional spheres. https://arxiv.org/abs/2412.02028

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