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

• 成果类型: Article
• 署名作者: Anderson, M; Katsuda, A; Kurylev, Y; Lassas, M; Taylor, M
• 署名单位: State University of New York (SUNY) System; Stony Brook University; Okayama University; Loughborough University; Aalto University; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0371-6
• 发表日期: 2004
• 页码: 261-321
• 关键词: unique continuation; MANIFOLDS; THEOREMS

摘要

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.