Extending a result of Chen, Erchenko and Gogolev

TL;DR

This paper extends a recent result by Chen, Erchenko, and Gogolev on embedding Riemannian manifolds with hyperbolic trapped sets into Anosov manifolds, removing some assumptions for broader applicability.

Contribution

It removes certain assumptions from the previous theorem, making the result applicable to all reasonable 3-dimensional cases.

Findings

Removed assumptions allow broader application

Extended the embedding result to more 3D examples

Clarified conditions under which the embedding holds

Abstract

In a recent paper, Chen, Erchenko and Gogolev have proven that if a Riemannian manifold with boundary has hyperbolic geodesic trapped set, then it can be embedded into a compact manifold whose geodesic flow is Anosov. They have to introduce some assumptions that we discuss here. We explain how some can be removed, obtaining in particular a result applicable to all reasonable 3 dimensional examples.