Area minimizers and boundary rigidity of almost hyperbolic metrics

DOI10.1215/00127094-2142529zbMath1271.53044arXiv1011.1570OpenAlexW1993514956MaRDI QIDQ2376815

Dmitri Burago, Sergei Ivanov

Publication date: 24 June 2013

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1570

zbMATH Keywords

boundary rigidityboundary distance functionarea minimizerstrict minimal filling

Mathematics Subject Classification ID

Integral geometry (53C65) Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24)

Related Items (10)

Rigidity of the Pu inequality and quadratic isoperimetric constants of normed spaces ⋮ Filling minimality and Lipschitz-volume rigidity of convex bodies among integral current spaces ⋮ Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into \(\mathbb{R}^n\) ⋮ Riemannian Anosov extension and applications ⋮ Local monotonicity of Riemannian and Finsler volume with respect to boundary distances ⋮ On filling minimality of simple Finsler manifolds ⋮ On Gromov-Hausdorff stability in a boundary rigidity problem ⋮ Simple Riemannian surfaces are scattering rigid ⋮ Determining a Riemannian metric from minimal areas ⋮ Open problems and questions about geodesics

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• On asymptotic volume of tori
• Two dimensional compact simple Riemannian manifolds are boundary distance rigid
• Volume comparison via boundary distances
• A rigidity theorem for simply connected manifolds without conjugate points

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