A SUPPORT THEOREM FOR THE GEODESIC RAY TRANSFORM OF SYMMETRIC TENSOR FIELDS

被引：19

作者：

Krishnan, Venkateswaran P. ^{[1
]}

Stefanov, Plamen ^{[2
]}

机构：

[1] Rensselaer Polytech Inst, Troy, NY 12180 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

INVERSE PROBLEMS AND IMAGING | 2009年 / 3卷 / 03期

基金：

美国国家科学基金会;

关键词：

integral geometry; X ray transform; tensors; support theorem; RADON TRANSFORMS; BOUNDARY RIGIDITY; INTEGRAL GEOMETRY; STABILITY;

D O I：

10.3934/ipi.2009.3.453

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (M, g) be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of such a field f along maximal geodesics vanish on an appropriate open subset of the space of geodesics in M. Under the assumption that the metric g is real-analytic, it is shown that there exists a vector field v satisfying f = dv on the set of points lying on these geodesics and v = 0 on the intersection of this set with the boundary partial derivative M of the manifold M. Using this result, a Helgason's type of a support theorem for the geodesic ray transform is proven. The approach is based on analytic microlocal techniques.

引用

页码：453 / 464

页数：12

共 20 条

[11] REAL ANALYTIC RADON TRANSFORMS ON RANK ONE SYMMETRICAL SPACES [J].