A sharp stability estimate for tensor tomography in non-positive curvature
Analysis of PDEs
2020-09-21 v2 Differential Geometry
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 , where the -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.
Cite
@article{arxiv.2001.04334,
title = {A sharp stability estimate for tensor tomography in non-positive curvature},
author = {Gabriel P. Paternain and Mikko Salo},
journal= {arXiv preprint arXiv:2001.04334},
year = {2020}
}
Comments
Revised version to appear in Mathematische Zeitschrift, 24p. The appendix of version 1 has been removed and incorporated in shorter form into the main text. The appendix still can be found in v1 and could be useful for other purposes