Analysis & PDE

  • Anal. PDE
  • Volume 9, Number 8 (2016), 1903-1930.

Invariant distributions and the geodesic ray transform

Gabriel P. Paternain and Hanming Zhou

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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.

Article information

Source
Anal. PDE, Volume 9, Number 8 (2016), 1903-1930.

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

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843378

Digital Object Identifier
doi:10.2140/apde.2016.9.1903

Mathematical Reviews number (MathSciNet)
MR3599521

Zentralblatt MATH identifier
1357.53088

Subjects
Primary: 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]
Secondary: 58J40: Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]

Keywords
geodesic ray transform first integral tensor tomography invariant distribution

Citation

Paternain, Gabriel P.; Zhou, Hanming. Invariant distributions and the geodesic ray transform. Anal. PDE 9 (2016), no. 8, 1903--1930. doi:10.2140/apde.2016.9.1903. https://projecteuclid.org/euclid.apde/1510843378


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