The Linearized Calderón Problem in Transversally Anisotropic Geometries
Ferreira, D. D. S., Kurylev, Y., Lassas, M., Liimatainen, T., & Salo, M. (2020). The Linearized Calderón Problem in Transversally Anisotropic Geometries. International Mathematics Research Notices, 2020(22), 8729-8765. https://doi.org/10.1093/imrn/rny234
Published inInternational Mathematics Research Notices
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 2018 the Authors
In this article we study the linearized anisotropic Calderón problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropic, we show that the boundary measurements determine an Fourier--Bros--Iagolnitzer-type transform at certain points in the transversal manifold. This leads to proving a uniqueness result for transversal singularities in the linearized problem. The method requires a geometric condition on the transversal manifold related to pairs of intersecting geodesics, but it does not involve the geodesic X-ray transform, which has limited earlier results on this problem.
PublisherOxford University Press
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