Boundary regularity for the Ricci equation, geometric convergence, and Gel’fand’s inverse boundary problem

By Michael T. Anderson, Atsushi Katsuda, Yaroslav Kurylev, Matti Lassas, Michael Taylor. 2002

157 citations recorded by the source corpus.

This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature bounds, on the manifold and its boundary, and a Lipschitz bound on the mean curvature of the boundary. The second is to establish geometric convergence of a (sub)sequence of manifolds with boundary with such geometrical bounds and also an upper bound on the diameter and a lower bound on injectivity and boundary injectivity radius, making use of the first part. The third theme involves the uniqueness and conditional stability of an inverse problem proposed by Gel’fand, making essential use of the results of the first two parts.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/66aaa3a08b0fe355cd8cde8c986abdcb670e453b

How researchers see this paper

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

In Computational Theory and Mathematics

1. Gunther Uhlmann
2. Plamen Stefanov
3. Lauri Oksanen
4. Matti Lassas
5. Yaroslav Kurylev
6. Katya Krupchyk
7. Mikko Salo
8. Carlos E. Kenig

In Mathematical Physics

1. Gunther Uhlmann
2. Plamen Stefanov
3. Matti Lassas
4. Yaroslav Kurylev
5. Lauri Oksanen
6. Mikko Salo
7. Katya Krupchyk
8. David dos Santos Ferreira

In Mechanics of Materials

1. Gunther Uhlmann
2. Plamen Stefanov
3. Yaroslav Kurylev
4. Matti Lassas
5. Lauri Oksanen
6. András Vasy
7. Gang Bao
8. Hai E Zhang

Citations in the corpus

• Inverse problem for the Riemannian wave equation with Dirichlet data and Neumann data on disjoint sets (2012, methodology): “For later development of the geometric boundary control method, see [2, 7, 27, 28, 31].”
• Rigidity of broken geodesic flow and inverse problems (2007, background): “[5], [26], [29] that the setR(M) possesses a natural structure of a Riemannian manifold with the map”
• Stable determination of generic simple metrics from the hyperbolic Dirichlet-to-Neumann map (2004, methodology): “wn functional analysis argument shows that under such compactness condition, the map g ! g (by identifying isometric metrics) must be continuous, once we know it is well-defined. This was exploited in [AKKLT] and minimal geometric conditions guaranteeing the compactness condition were established the”