Boundary rigidity and stability for generic simple metrics

DOI10.1090/S0894-0347-05-00494-7zbMath1079.53061arXivmath/0408075OpenAlexW2169251826MaRDI QIDQ5313366

Publication date: 29 August 2005

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0408075

zbMATH Keywords

Riemannian manifold boundary rigidity simple metric s-injectivity

Mathematics Subject Classification ID

Integral geometry (53C65) Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

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Cites Work