3 research outputs found
Limiting Carleman weights and anisotropic inverse problems
In this article we consider the anisotropic Calderon problem and related
inverse problems. The approach is based on limiting Carleman weights,
introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean
case. We characterize those Riemannian manifolds which admit limiting Carleman
weights, and give a complex geometrical optics construction for a class of such
manifolds. This is used to prove uniqueness results for anisotropic inverse
problems, via the attenuated geodesic X-ray transform. Earlier results in
dimension were restricted to real-analytic metrics.Comment: 58 page