The inverse problem for the local geodesic ray transform
نویسندگان
چکیده
منابع مشابه
The Inverse Problem for the Local Geodesic Ray Transform
Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces the geodesic X-ray transform is globally injective. In addition we prove sta...
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15 صفحه اولInverting the Local Geodesic X-ray Transform on Tensors
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 wh...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2015
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-015-0631-7