Stefanov, Plamen Microlocal approach to tensor tomography and boundary and lens rigidity. (English) Zbl 1199.53099 Serdica Math. J. 34, No. 1, 67-112 (2008). 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 Cited in 9 Documents MSC: 53C24 Rigidity results 53C65 Integral geometry 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions Keywords:Boundary rigidity; tensor tomography; inverse problems PDFBibTeX XMLCite \textit{P. Stefanov}, Serdica Math. J. 34, No. 1, 67--112 (2008; Zbl 1199.53099)