### 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 language | English |
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Pages (from-to) | 69-79 |

Number of pages | 11 |

Journal | Electronic Research Announcements of the American Mathematical Society |

Volume | 9 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2 2003 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Electronic Research Announcements of the American Mathematical Society*,

*9*(9), 69-79. https://doi.org/10.1090/S1079-6762-03-00113-6

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

Research output: Contribution to journal › Article

*Electronic Research Announcements of the American Mathematical Society*, vol. 9, no. 9, pp. 69-79. https://doi.org/10.1090/S1079-6762-03-00113-6

}

TY - JOUR

T1 - Metric tensor estimates, geometric convergence, and inverse boundary problems

AU - Anderson, Michael

AU - Katsuda, Atsushi

AU - Kurylev, Yaroslav

AU - Lassas, Matti

AU - Taylor, Michael

PY - 2003/9/2

Y1 - 2003/9/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=15944383828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=15944383828&partnerID=8YFLogxK

U2 - 10.1090/S1079-6762-03-00113-6

DO - 10.1090/S1079-6762-03-00113-6

M3 - Article

AN - SCOPUS:15944383828

VL - 9

SP - 69

EP - 79

JO - Electronic Research Announcements in Mathematical Sciences

JF - Electronic Research Announcements in Mathematical Sciences

SN - 1935-9179

IS - 9

ER -