Inverting the local geodesic X-ray transform on tensors

By Plamen Stefanov, Gunther Uhlmann, András Vasy. Journal d'Analyse Mathematique, 2014

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We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n ≥ 3. We also present an inversion formula. Under the condition that the manifold can be foliated with a continuous family of strictly convex surfaces, we prove a global result which also implies a lens rigidity result near such a metric. The class of manifolds satisfying the foliation condition includes manifolds with no focal points, and does not exclude existence of conjugate points.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a54d2f9425da9db43b55567c5086be3dfa8d511e

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In Applied Mathematics

In Astronomy and Astrophysics

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Citations in the corpus

Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge (2017, methodology): “r, 2A j i is close to j i if one is suciently close to the boundary of the domain. Thus, considering the resulting transform N~ z on the ncomponents u0= (u1;:::;u n), with u= e z=xf, we get, as in [27], in this case using Theorem 6.3, that there is c0 >0 such that for 0 <c<c0, (7.16) ku0k ”