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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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

geodesic ray transform first integral tensor tomography invariant distribution


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.

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