Metric tensor estimates, geometric convergence, and inverse boundary problems

Michael Anderson, Atsushi Katsuda, Yaroslav Kurylev, Matti Lassas, Michael Taylor

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)69-79
Number of pages11
JournalElectronic Research Announcements of the American Mathematical Society
Volume9
Issue number9
DOIs
Publication statusPublished - Sep 2 2003

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Geometric Convergence
Boundary Problem
Inverse Problem
Tensor
Injectivity
Manifolds with Boundary
Metric
Estimate
Conditional Stability
Ricci Curvature
Mean Curvature
Subsequence
Lipschitz
Uniqueness
Regularity
Radius
Lower bound
Upper bound

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Metric tensor estimates, geometric convergence, and inverse boundary problems. / Anderson, Michael; Katsuda, Atsushi; Kurylev, Yaroslav; Lassas, Matti; Taylor, Michael.

In: Electronic Research Announcements of the American Mathematical Society, Vol. 9, No. 9, 02.09.2003, p. 69-79.

Research output: Contribution to journalArticle

Anderson, Michael ; Katsuda, Atsushi ; Kurylev, Yaroslav ; Lassas, Matti ; Taylor, Michael. / Metric tensor estimates, geometric convergence, and inverse boundary problems. In: Electronic Research Announcements of the American Mathematical Society. 2003 ; Vol. 9, No. 9. pp. 69-79.
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