Showing items with similar title or keywords.

• On Radon transforms on compact Lie groups 

  Ilmavirta, Joonas (American Mathematical Society, 2016)

  We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S 1 nor to S 3 . This is true for both smooth functions and ...

• Geometric Inverse Problems : With Emphasis on Two Dimensions 

  Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther (Cambridge University Press, 2023)

  This up-to-date treatment of recent developments in geometric inverse problems introduces graduate students and researchers to an exciting area of research. With an emphasis on the two-dimensional case, topics covered ...

• X-ray Transforms in Pseudo-Riemannian Geometry 

  Ilmavirta, Joonas (Springer US, 2018)

  We study the problem of recovering a function on a pseudo-Riemannian manifold from its integrals over all null geodesics in three geometries: pseudo-Riemannian products of Riemannian manifolds, Minkowski spaces, and tori. ...

• The X-Ray Transform for Connections in Negative Curvature 

  Guillarmou, Colin; Paternain, Gabriel P.; Salo, Mikko; Uhlmann, Gunther (Springer Berlin Heidelberg, 2016)

  We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without ...

• The Light Ray Transform in Stationary and Static Lorentzian Geometries 

  Feizmohammadi, Ali; Ilmavirta, Joonas; Oksanen, Lauri (Springer, 2021)

  Given a Lorentzian manifold, the light ray transform of a function is its integrals along null geodesics. This paper is concerned with the injectivity of the light ray transform on functions and tensors, up to the natural ...