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arXiv · 2009.13665

Riemannian Anosov extension and applications

Dong Chen·Alena Erchenko·Andrey Gogolev
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Abstract

Let $\Sigma$ be a Riemannian manifold with strictly convex spherical boundary. Assuming absence of conjugate points and that the trapped set is hyperbolic, we show that $\Sigma$ can be isometrically embedded into a closed Riemannian manifold with Anosov geodesic flow. We use this embedding to provide a direct link between the classical Livshits theorem for Anosov flows and the Livshits theorem for the X-ray transform which appears in the boundary rigidity program. Also, we give an application for lens rigidity in a conformal class.

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Dong Chen, Alena Erchenko, Andrey Gogolev. 2020-09-28. Riemannian Anosov extension and applications. https://arxiv.org/abs/2009.13665

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