Limiting Carleman weights and anisotropic inverse problems |
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| Authors: | David Dos Santos Ferreira Carlos E Kenig Mikko Salo Gunther Uhlmann |
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| Institution: | (1) LAGA, Mathématique, Université Paris 13, 93430 Villetaneuse, France;(2) Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637-1514, USA;(3) Department of Mathematics and Statistics, University of Helsinki, 00014 Helsinki, Finland;(4) Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA |
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| Abstract: | In this article we consider the anisotropic Calderón problem and related inverse problems. The approach is based on limiting
Carleman weights, introduced in Kenig et al. (Ann. Math. 165:567–591, 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 ray transform. Earlier results in dimension n≥3 were restricted to real-analytic metrics. |
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