Tensor tomography on surfaces

2011/09/02 by Paternain, Gabriel P., Salo, Mikko, Uhlmann, Gunther · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.0505

Abstract

We show that on simple surfaces the geodesic ray transform acting on solenoidal symmetric tensor fields of arbitrary order is injective. This solves a long standing inverse problem in the two-dimensional case.

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• The Pestov identity on the frame bundle and associated homogeneous fibrations
• The matrix weighted real-analytic double fibration transforms

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