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2016 Invariant distributions and the geodesic ray transform
Gabriel P. Paternain, Hanming Zhou
Anal. PDE 9(8): 1903-1930 (2016). DOI: 10.2140/apde.2016.9.1903

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.

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Gabriel P. Paternain. Hanming Zhou. "Invariant distributions and the geodesic ray transform." Anal. PDE 9 (8) 1903 - 1930, 2016. https://doi.org/10.2140/apde.2016.9.1903

Information

Received: 18 November 2015; Revised: 28 July 2016; Accepted: 12 September 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1357.53088
MathSciNet: MR3599521
Digital Object Identifier: 10.2140/apde.2016.9.1903

Subjects:
Primary: 53C65
Secondary: 58J40

Keywords: first integral , geodesic ray transform , Invariant distribution , tensor tomography

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.9 • No. 8 • 2016
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