9 papers
Density of Products of Solutions and the Linearized Calderón Problem in an Analytic Background
Leonard Busch, Tony Liimatainen, Gunther Uhlmann
We study the linearization, with respect to zeroth-order perturbations, of the local Dirichlet-to-Neumann map of a formally self-adjoint elliptic operator on a compact R…
Determination of hyperelastic parameters with non-trapping wavespeeds
Gunther Uhlmann, Jian Zhai
We consider the elastic wave equation in three-dimensional isotropic medium with up to quadratic nonlinear terms. We show that five out of the six elastic parameters can be uniquel…
The Calderón problem for near-Euclidean metrics
Gunther Uhlmann, Yiran Wang
In this article, we consider the anisotropic Calderón problem of determining the potential from boundary measurements of the time-independent Schrödinger equation on compact Rieman…
The linearized minimal surfaces problem
Haim Grebnev, Plamen Stefanov, Gunther Uhlmann +1
We characterize the kernel of the linearization of the minimal surface problem about the Euclidean metric in a bounded smooth domain , , with the b…
The partial data Calderón problem in dimension three
Gunther Uhlmann, Yiran Wang
We consider an inverse boundary value problem for the time-independent Schrödinger equation in dimension three. We prove that the local Dirichlet-to-Neumann map defined near a boun…
The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography
Alberto Enciso, Gunther Uhlmann, Michał Wrochna
We consider the Klein-Gordon equation on asymptotically anti-de Sitter spacetimes, and show that the forward Dirichlet-to-Neumann map (or scattering matrix) is a fractional power o…
On the anisotropic Calderón's problem
Gunther Uhlmann, Jian Zhai
We prove that the Riemannian metric on a compact manifold of dimension with smooth boundary can be uniquely determined, up to an isometry fixing the boundary, by the Diri…
Invertibility of local geodesic transverse and mixed ray transforms II: higher order tensors
Gunther Uhlmann, Jian Zhai
Consider a compact Riemannian manifold in dimension with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of …
Invertibility of local geodesic transverse and mixed ray transforms I: basic cases
Gunther Uhlmann, Jian Zhai
Consider a compact Riemannian manifold in dimension with strictly convex boundary. We show that the transverse ray transform of tensors and the mixed ray transform of…