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

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

研究成果: ジャーナルへの寄稿記事

60 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)261-321
ページ数61
ジャーナルInventiones Mathematicae
158
発行部数2
DOI
出版物ステータス出版済み - 1 1 2004
外部発表Yes

Fingerprint

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem. / Anderson, Michael; Katsuda, Atsushi; Kurylev, Yaroslav; Lassas, Matti; Taylor, Michael.

:: Inventiones Mathematicae, 巻 158, 番号 2, 01.01.2004, p. 261-321.

研究成果: ジャーナルへの寄稿記事

Anderson, Michael ; Katsuda, Atsushi ; Kurylev, Yaroslav ; Lassas, Matti ; Taylor, Michael. / Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem. :: Inventiones Mathematicae. 2004 ; 巻 158, 番号 2. pp. 261-321.
@article{0f93dffee35c4885aafa6135ee0746b8,
title = "Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem",
abstract = "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.",
author = "Michael Anderson and Atsushi Katsuda and Yaroslav Kurylev and Matti Lassas and Michael Taylor",
year = "2004",
month = "1",
day = "1",
doi = "10.1007/s00222-004-0371-6",
language = "English",
volume = "158",
pages = "261--321",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem

AU - Anderson, Michael

AU - Katsuda, Atsushi

AU - Kurylev, Yaroslav

AU - Lassas, Matti

AU - Taylor, Michael

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=7644221981&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=7644221981&partnerID=8YFLogxK

U2 - 10.1007/s00222-004-0371-6

DO - 10.1007/s00222-004-0371-6

M3 - Article

AN - SCOPUS:7644221981

VL - 158

SP - 261

EP - 321

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 2

ER -