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We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n>=3.
Über die Elastizitaet der Erde bei Beruecksichtigung ihrer variablen Dichte
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E. Wiechert and K. Zoeppritz · 1907
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R. G Mukhometov · 1975
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A problem of integral geometry for a family of geodesics and an inverse kinematic seismics problem
I. N. Bernstein and M. L. Gerver · 1978
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On a problem of reconstructing Riemannian metrics
R. G. Muhometov · 1981
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Support theorems for real-analytic Radon transforms
Jan Boman and Eric Todd Quinto · 1987
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Integral geometry of tensor fields on a manifold of negative curvature
L. N. Pestov and V. A. Sharafutdinov · 1988
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Integral geometry of tensor fields
V. A. Sharafutdinov · 1994
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Geometric scattering theory
Richard B. Melrose · 1995
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On uniqueness of determination of a form of first degree by its integrals along geodesics
Yu. E. Anikonov and V. G. Romanov · 1997
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Ray transform on Riemannian manifolds, lecture notes, UW–Seattle
V. A. Sharafutdinov · 1999
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Convexity of spheres in a manifold without conjugate points
Akhil Ranjan and Hemangi Shah · 2002
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A problem in integral geometry in a nonconvex domain
V. A. Sharafutdinov · 2002
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Conjugacy rigidity for non-positively curved graph manifolds
Christopher B. Croke · 2004
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Stability estimates for the X-ray transform of tensor fields and boundary rigidity
Plamen Stefanov and Gunther Uhlmann · 2004
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Two dimensional compact simple Riemannian manifolds are boundary distance rigid
Leonid Pestov and Gunther Uhlmann · 2005
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Integral geometry of tensor fields on a class of non-simple Riemannian manifolds
Plamen Stefanov and Gunther Uhlmann · 2008
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A support theorem for the geodesic ray transform on functions
Venkateswaran P. Krishnan · 2009
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A support theorem for the geodesic ray transform of symmetric tensor fields
Venkateswaran P. Krishnan and Plamen Stefanov · 2009
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Local lens rigidity with incomplete data for a class of non-simple Riemannian manifolds
Plamen Stefanov and Gunther Uhlmann · 2009
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Scattering rigidity with trapped geodesics
Christopher Croke · 2012
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Lens rigidity with trapped geodesics in two dimensions
Christopher Croke and Pillar Herreros · 2012
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