Résume | We consider the following geometric inverse problem: Consider a simply connected Riemannian 3-manifold (M,𝑔) with boundary. Assume that given any closed loop γ on the boundary, one knows the areas of the corresponding minimal surfaces with boundary γ. Then from this information can one reconstruct the metric 𝑔? We answer this in the affirmative in many cases. We will briefly discuss the relation of this problem with the question of reconstructing a metric from lengths of geodesics, and also with the Calderon problem of reconstructing a metric from the Dirichlet-to-Neumann operator for the corresponding Laplace-Beltrami operator. Joint with T. Balehowsky and A. Nachman. |