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arXiv · 2001.04334

A sharp stability estimate for tensor tomography in non-positive curvature

Gabriel P. Paternain·Mikko Salo
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Abstract

We consider the geodesic X-ray transform acting on solenoidal tensor fields on a compact simply connected manifold with strictly convex boundary and non-positive curvature. We establish a stability estimate of the form $L^2\mapsto H^{1/2}_{T}$, where the $H^{1/2}_{T}$-space is defined using the natural parametrization of geodesics as initial boundary points and incoming directions (fan-beam geometry); only tangential derivatives at the boundary are used. The proof is based on the Pestov identity with boundary term localized in frequency.

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Gabriel P. Paternain, Mikko Salo. 2020-01-13. A sharp stability estimate for tensor tomography in non-positive curvature. https://arxiv.org/abs/2001.04334

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