Browsing Cambridge University by Author "Paternain, Gabriel Pedro"
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INVARIANT DISTRIBUTIONS AND THE GEODESIC RAY TRANSFORM
Paternain, Gabriel Pedro; Zhou, Hanming (Mathematical Science PublishersAnalysis & PDE, 2016-12-11)We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $\textit{m}$-tensors and the existence of invariant distributions or smooth first integrals with ...
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Invariant distributions, Beurling transforms and tensor tomography in higher dimensions
Paternain, Gabriel Pedro; Salo, Mikko; Uhlmann, Gunther (SpringerMathematische Annalen, 2015-02-01)In the recent articles [PSU13, PSU14c], a number of tensor tomography results were proved on two-dimensional manifolds. The purpose of this paper is to extend some of these methods to manifolds of any dimension. A central ...
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The contact property for magnetic flows on surfaces
Benedetti, Gabriele (University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 2015-01-06)This work investigates the dynamics of magnetic flows on closed orientable Riemannian surfaces. These flows are determined by triples (M, g, σ), where M is the surface, g is the metric and σ is a 2-form on M . Such dynamical ...
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The geodesic X-ray transform with a $GL(n,\mathbb{C})$-connection
Monard, François; Paternain, Gabriel PedroWe derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of such all transforms in a neighbourhood of constant ...
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The X-ray transform for connections in negative curvature
Guillarmou, Colin; Paternain, Gabriel Pedro; Salo, Mikko; Uhlmann, Gunther (SpringerCommunications in Mathematical Physics, 2015-11-23)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 boundary, ...