Vol. 14, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Classical and microlocal analysis of the x-ray transform on Anosov manifolds

Sébastien Gouëzel and Thibault Lefeuvre

Vol. 14 (2021), No. 1, 301–322
Abstract

We complete the microlocal study of the geodesic x-ray transform on Riemannian manifolds with Anosov geodesic flow initiated by Guillarmou (J. Differential Geom. 105:2 (2017), 177–208) and pursued by Guillarmou and Lefeuvre in (Ann. of Math. (2) 190:1 (2019), 321–344). We prove new stability estimates and clarify some properties of the operator Πm — the generalized x-ray transform. These estimates rely on a refined version of the Livšic theorem for Anosov flows, especially on a new quantitative finite-time Livšic theorem.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 35.173.234.169 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
Anosov flow, hyperbolic dynamical systems, x-ray transform, microlocal analysis
Mathematical Subject Classification 2010
Primary: 37C27, 37D40, 53C21, 53C22, 53C24
Milestones
Received: 17 May 2019
Revised: 9 August 2019
Accepted: 7 October 2019
Published: 19 February 2021
Authors
Sébastien Gouëzel
Laboratoire Jean Leray, CNRS UMR 6629
Université de Nantes
Nantes
France
Thibault Lefeuvre
Laboratoire de Mathématiques d’Orsay
Université Paris-Sud, CNRS
Université Paris-Saclay
Orsay
France