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Article · Inverse Problems · February 28, 2006

Integral geometry problem for nontrapping manifolds

Nurlan Dairbekov
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Abstract

We consider the integral geometry problem of restoring a tensor field on a manifold with boundary from its integrals over geodesics running between boundary points. For nontrapping manifolds with a certain upper curvature bound, we prove that a tensor field, integrating to zero over geodesics between boundary points, is potential. For functions and 1-forms, this is shown to be true for arbitrary nontrapping manifolds with no conjugate points. As a consequence, we also establish deformation boundary rigidity for strongly geodesic minimizing manifolds with a certain upper curvature bound.

Numerical methods in inverse problemsSpectral Theory in Mathematical PhysicsAdvanced Differential Geometry Researchintegral geometrygeodesicstensor fields

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