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Microlocal approach to tensor tomography and boundary and lens rigidity. (English) Zbl 1199.53099

This is a survey article where the author discusses some recent results with Gunther Uhlmann on the boundary rigidity problem (is it possible to recover the topology on a compact Riemannian manifold with boundary from the boundary distance function?) and on the associated tensor tomography problem (is it possible to recover a tensor field from its integrals along geodesics connecting boundary points?). The Dirichlet-to- Neumann map on Riemannian manifolds with boundary is also studied.
Reviewer: Georgi Vodev

MSC:

53C24 Rigidity results
53C65 Integral geometry
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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