Abstract
We prove that a -generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. As a consequence, we prove the -stability conjecture for Riemannian geodesic flows of closed surfaces: a -structurally stable Riemannian geodesic flow of a closed surface is Anosov. In order to prove these statements, we establish a general result that may be of independent interest and provides sufficient conditions for a Reeb flow of a closed 3-manifold to be Anosov.
Citation
Gonzalo Contreras. Marco Mazzucchelli. "Proof of the -stability conjecture for geodesic flows of closed surfaces." Duke Math. J. 173 (2) 347 - 390, 1 February 2024. https://doi.org/10.1215/00127094-2023-0010
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