6533b834fe1ef96bd129d614
RESEARCH PRODUCT
The Linearized Calderón Problem in Transversally Anisotropic Geometries
David Dos Santos FerreiraTony LiimatainenMikko SaloMatti LassasYaroslav Kurylevsubject
Mathematics - Differential GeometryGeodesicGeneral MathematicsNEUMANN MAPBoundary (topology)Type (model theory)01 natural scienceslaw.inventionMathematics - Analysis of PDEslinearized anisotropic Calderón problemlaw35R30 35J25111 MathematicsFOS: Mathematics0101 mathematicsMathematics010102 general mathematicsMathematical analysisInverse problem010101 applied mathematicsHarmonic functionDifferential Geometry (math.DG)Transversal (combinatorics)Gravitational singularityMathematics::Differential GeometryINVERSE PROBLEMManifold (fluid mechanics)Analysis of PDEs (math.AP)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-12-13 |