Limiting Carleman weights and anisotropic inverse problems

作者：Ferreira David Dos Santos^*; Kenig Carlos E; Salo Mikko; Uhlmann Gunther

来源：Inventiones Mathematicae, 2009, 178(1): 119-171.

DOI：10.1007/s00222-009-0196-4

In this article we consider the anisotropic Calderon 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.

• 出版日期2009-10