Vol. 9, No. 8, 2016

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Invariant distributions and the geodesic ray transform

Gabriel P. Paternain and Hanming Zhou

Vol. 9 (2016), No. 8, 1903–1930
Abstract

We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric m-tensors and the existence of invariant distributions or smooth first integrals with prescribed projection over the set of solenoidal m-tensors. We work with compact simple manifolds, but several of our results apply to nontrapping manifolds with strictly convex boundary.

Keywords
geodesic ray transform, first integral, tensor tomography, invariant distribution
Mathematical Subject Classification 2010
Primary: 53C65
Secondary: 58J40
Milestones
Received: 18 November 2015
Revised: 28 July 2016
Accepted: 12 September 2016
Published: 11 December 2016
Authors
Gabriel P. Paternain
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Cambridge CB3 0WB
United Kingdom
Hanming Zhou
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Cambridge CB3 0WB
United Kingdom