# A New Proof of the Existence of Embedded Surfaces with Anosov Geodesic Flow

*2018, Volume 23, Number 6, pp. 685-694*

Author(s):

**Donnay V., Visscher D.**

We give a new proof of the existence of compact surfaces embedded in $\mathbb{R}^3$ with Anosov geodesic flows. This proof starts with a noncompact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of

explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov.

explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov.

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