Geodesic
Metric tensor estimates, geometric convergence, and inverse boundary problems
Anderson, Michael1 ; Katsuda, Atsushi2 ; Kurylev, Yaroslav3 ; Lassas, Matti4 ; Taylor, Michael5
1 Mathematics Department, State University of New York, Stony Brook, NY 11794
2 Mathematics Department, Okayama University, Tsushima-naka, Okayama, 700-8530, Japan
3 Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
4 Rolf Nevanlinna Institute, University of Helsinki, FIN-00014, Finland
5 Mathematics Deptartment, University of North Carolina, Chapel Hill, NC 27599
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 69-79.

Voir la notice de l'article provenant de la source American Mathematical Society

Three themes are treated in the results announced here. The first is the 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 the 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.
DOI : 10.1090/S1079-6762-03-00113-6

Anderson, Michael 1 ; Katsuda, Atsushi 2 ; Kurylev, Yaroslav 3 ; Lassas, Matti 4 ; Taylor, Michael 5

1 Mathematics Department, State University of New York, Stony Brook, NY 11794
2 Mathematics Department, Okayama University, Tsushima-naka, Okayama, 700-8530, Japan
3 Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
4 Rolf Nevanlinna Institute, University of Helsinki, FIN-00014, Finland
5 Mathematics Deptartment, University of North Carolina, Chapel Hill, NC 27599 
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Anderson, Michael; Katsuda, Atsushi; Kurylev, Yaroslav; Lassas, Matti; Taylor, Michael. Metric tensor estimates, geometric convergence, and inverse boundary problems. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 69-79. doi : 10.1090/S1079-6762-03-00113-6. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00113-6/

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