Two dimensional compact simple Riemannian manifolds are boundary distance rigid

• 成果类型: Article
• 署名作者: Pestov, L; Uhlmann, G
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.161.1093
• 发表日期: 2005
• 页码: 1093-1110
• 关键词: negative curvature; geodesics; length

摘要

We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.