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arXiv · 2607.08439

Construction and upper bound on the minimum genus of an embedded surface with Anosov geodesic flow

Victor Donnay·Daniel Visscher
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Abstract

We create examples of smooth, compact surfaces in $R^3$ for which the geodesic flow is Anosov. We determine their genus, thereby giving a (non-sharp) upper bound for the minimal genus of an embedded surface with Anosov geodesic flow. These examples are explicit physically realizable Anosov systems.

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Victor Donnay, Daniel Visscher. 2026-07-09. Construction and upper bound on the minimum genus of an embedded surface with Anosov geodesic flow. https://arxiv.org/abs/2607.08439

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