On determining a Riemannian manifold from the Dirichlet-to-Neumann map

By BY Matti Lassas, Gunther Uhlmann. 2001

248 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/405674c877ebe061af54926e029c0a8767e20eef

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Yi-Hsuan Lin
2. Matti Lassas
3. Gunther Uhlmann
4. Mikko Salo
5. Lauri Oksanen
6. Carlos E. Kenig
7. David dos Santos Ferreira
8. T. Liimatainen

In Electrical and Electronic Engineering

1. Mikko Salo
2. Yi-Hsuan Lin
3. Matti Lassas
4. David dos Santos Ferreira
5. Mikhail I. Belishev
6. Gunther Uhlmann
7. Carlos E. Kenig
8. T. Liimatainen

In Mathematical Physics

1. Gunther Uhlmann
2. Mikko Salo
3. Matti Lassas
4. Lauri Oksanen
5. David dos Santos Ferreira
6. Carlos E. Kenig
7. Yi-Hsuan Lin
8. C. Guillarmou

Citations in the corpus

• Limiting Carleman weights and anisotropic inverse problems (2008, methodology): “Lassas and Uhlmann [17] proved that (1.1) is the only obstruction to unique identifiability of the metric for real-analytic manifolds in dimension n ≥ 3.”
• Recent progress in the boundary control method (2007, background): “4 Uniqueness of determination was shown by Lassas and Uhlmann in [80].”
• Calderon inverse Problem with partial data on Riemann Surfaces (2009, background): “…results in the direction of recovering the Riemannian manifold (Ω, g) when V = 0, for instance the surface case by Lassas-Uhlmann [21] (see also [4, 15]), the real-analytic manifold case by Lassas-Taylor-Uhlmann [20] (see also [14] for the Einstein case), the case of manifolds admitting…”
• Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets (2012, background): “nd Uhlmann [29]. Also, the local data problem for anisotropic elliptic equations in ˆR2 was recently solved by Imanuvilov, Uhlmann and Yamamoto [23, 24]. For two-dimensional manifolds it was shown in [35] that the local boundary data for the Laplace-Beltrami equation with S= R6= @Mdetermines uniquel”
• Inverse problems for elliptic equations with power type nonlinearities (2019, methodology): “ditions as above. For the linear equation ∆gu + qu = 0, an analogous result has been proved when M is a domain in R2 with a Riemannian metric [IUY12], when M is a manifold and the potentials are zero [LU01], and when the manifold M is a priori known [GT11]. The recovery of properties of both the man”