The Linearized Calderón Problem in Transversally Anisotropic Geometries
The Linearized Calderón Problem in Transversally Anisotropic Geometries
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DOI：
10.1093/imrn/rny234
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发表时间：
2017-12
影响因子：
1
通讯作者：
D. D. S. Ferreira-D.;Y. Kurylev;M. Lassas;Tony Liimatainen;M. Salo
中科院分区：
文献类型：
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作者：
D. D. S. Ferreira-D.;Y. Kurylev;M. Lassas;Tony Liimatainen;M. Salo
本文研究线性化各向异性Calderon问题。在有边界的紧致流形中，这个问题相当于证明调和函数的乘积形成一个完备集。假设流形是横向各向异性的，我们表明，边界测量确定FBI型变换在某些点的横向流形。这导致恢复的线性化问题中的横向奇异性。该方法需要一个几何条件的横截流形有关的对相交测地线，但它不涉及测地X射线变换，这限制了早期的结果在这个问题上。
In this article we study the linearized anisotropic Calderon 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 FBI type transform at certain points in the transversal manifold. This leads to recovery of 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.