Displaying similar documents to “Recent progress on the boundary rigidity problem.”

On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

Yuri E. Gliklikh, Andrei V. Obukhovski (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.

Inverse Problems: Visibility and Invisibility

Gunther Uhlmann (2012)

Journées Équations aux dérivées partielles

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This survey article expands on the lectures given at Biarritz in June, 2012, on “Inverse Problems: Visibility and Invisibility". The first inverse problem we consider is whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. This is called electrical impedance tomography (EIT) and also Calderón’s problem since the famous analyst proposed it in the mathematical literature []. The second is on travel time tomography....

The Ruelle rotation of Killing vector fields

Konstantin Athanassopoulos (2009)

Colloquium Mathematicae

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We present an explicit formula for the Ruelle rotation of a nonsingular Killing vector field of a closed, oriented, Riemannian 3-manifold, with respect to Riemannian volume.