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arXiv · 2311.12979

The stability conjecture for geodesic flows of compact manifolds without conjugate points and quasi-convex universal covering

Rafael Potrie·Rafael O. Ruggiero
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Abstract

Let $(M,g)$ be a $C^{\infty}$ compact, boudaryless connected manifold without conjugate points with quasi-convex universal covering and divergent geodesic rays. We show that the geodesic flow of $(M,g)$ is $C^{2}$-structurally stable from Ma\~{n}\'{e}'s viewpoint if and only if it is an Anosov flow, proving the so-called $C^{1}$-stability conjecture.

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Rafael Potrie, Rafael O. Ruggiero. 2023-11-21. The stability conjecture for geodesic flows of compact manifolds without conjugate points and quasi-convex universal covering. https://arxiv.org/abs/2311.12979

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