RIEMANNIAN ANOSOV EXTENSION AND APPLICATIONS

Dong Chen, Alena Erchenko, Andrey Gogolev

Research output: Contribution to journalArticlepeer-review

Abstract

Let Σ be a Riemannian manifold with strictly convex spherical boundary. Assuming absence of conjugate points and that the trapped set is hyperbolic, we show that Σ 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.

Original languageEnglish (US)
Pages (from-to)945-987
Number of pages43
JournalJournal de l'Ecole Polytechnique - Mathematiques
Volume10
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

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