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Metric tensor estimates, geometric convergence, and inverse boundary problems
Author(s):
Michael
Anderson;
Atsushi
Katsuda;
Yaroslav
Kurylev;
Matti
Lassas;
Michael
Taylor
Journal:
Electron. Res. Announc. Amer. Math. Soc.
9
(2003),
69-79.
MSC (2000):
Primary 35J25, 47A52, 53C21
Posted:
September 2, 2003
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Abstract:
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.
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Additional Information:
Michael
Anderson
Affiliation:
Mathematics Department, State University of New York, Stony Brook, NY 11794
Email:
anderson@math.sunysb.edu
Atsushi
Katsuda
Affiliation:
Mathematics Department, Okayama University, Tsushima-naka, Okayama, 700-8530, Japan
Email:
katsuda@math.okayama-u.ac.jp
Yaroslav
Kurylev
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK
Email:
Y.V.Kurylev@lboro.ac.uk
Matti
Lassas
Affiliation:
Rolf Nevanlinna Institute, University of Helsinki, FIN-00014, Finland
Email:
lassas@cc.helsinki.fi
Michael
Taylor
Affiliation:
Mathematics Deptartment, University of North Carolina, Chapel Hill, NC 27599
Email:
met@math.unc.edu
DOI:
10.1090/S1079-6762-03-00113-6
PII:
S 1079-6762(03)00113-6
Keywords:
Ricci tensor,
harmonic coordinates,
geometric convergence,
inverse problems,
conditional stability
Received by editor(s):
December 17, 2002
Posted:
September 2, 2003
Communicated by:
Tobias Colding
Copyright of article:
Copyright
2003,
American Mathematical Society
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