Local X-ray Transform on Asymptotically Hyperbolic Manifolds via Projective Compactification

Abstract

We prove local injectivity near a boundary point for the geodesic X-ray transform for an asymptotically hyperbolic metric even mod $O({\rho }^5)$ in dimensions three and higher.

arXiv comment30 pages. v2: Final version. Minor editorial changes. Dedication and memorial added

References in corpus (4)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Projective Compactifications and Einstein metrics
• Microlocal analysis of asymptotically hyperbolic spaces and high energy resolvent estimates
• Projective Compactness and Conformal Boundaries

Cited by in corpus (4)

• Broken ray transform for twisted geodesics on surfaces with a reflecting obstacle
• Stability Estimates for the X-Ray Transform on Simple Asymptotically Hyperbolic Manifolds
• Double b-fibrations and desingularization of the X-ray transform on manifolds with strictly convex boundary
• The hyperbolic X-ray transform: new range characterizations, mapping properties and functional relations