34 citations · 39 across the 6 of their papers we have counts for
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The Calderón problem on Riemannian surfaces and of minimal surfaces
Cătălin I. Cârstea, Tony Liimatainen, Leo Tzou
In this paper we prove two results. The first shows that the Dirichlet-Neumann map of the operator on a Riemannian surface can determine its topological, differential, and…
An inverse problem for general minimal surfaces
Cătălin I. Cârstea, Matti Lassas, Tony Liimatainen +1
In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if is a -dimensio…
Determining Lorentzian manifold from non-linear wave observation at a single point
Medet Nursultanov, Lauri Oksanen, Leo Tzou
We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evalu…
A general support theorem for analytic double fibration transforms
Marco Mazzucchelli, Mikko Salo, Leo Tzou
We develop a systematic approach for resolving the analytic wave front set for a class of integral geometry transforms appearing in various tomography problems. Combined with micro…
Eigenvalue Variations of the Neumann Laplace Operator Due to Perturbed Boundary Conditions
Medet Nursultanov, William Trad, Justin Tzou +1
This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold under the singular perturbation. This perturbation involve…
The Carleman estimate and a partial data inverse problem
Francis J. Chung, Leo Tzou
We construct an explicit Green's function for the conjugated Laplacian , which let us control our solutions on roughly half of the boundary. We app…