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: Contribution to journalArticle査読

67 被引用数 (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.

本文言語英語
ページ(範囲)261-321
ページ数61
ジャーナルInventiones Mathematicae
158
2
DOI
出版ステータス出版済み - 2004
外部発表はい

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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