JOINT INVERSE PROBLEMS AND DIFFERENTIAL GEOMETRY/PDE SEMINAR

Tuesday, July 6, 2004 Padelford C-36 1:30 pm Boundary rigidity of Riemannian manifolds

Plamen Stefanov (Purdue University)

This talk is based on a joint work with Gunther Uhlmann. Let (M,g) be a compact Riemannian manifold with boundary. We study the inverse problem of recovering g (up to an isometry) from the distance function d(x, y) known for all boundary points. The linearized problem is recovery of a tensor (up to a potential field) from the geodesic X-ray transform. We show that there is global uniqueness and Holder stability for generic simple metrics. To this end, we prove uniqueness and a stability estimate with loss of one derivative for the linear problem for an open dense set of simple metrics including all real analytic (simple) ones.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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