Abstract
Let be a compact Riemannian manifold with boundary. We show that is Gromov–Hausdorff close to a convex Euclidean region of the same dimension if the boundary distance function of is –close to that of . More generally, we prove the same result under the assumptions that the boundary distance function of is –close to that of , the volumes of and are almost equal, and volumes of metric balls in have a certain lower bound in terms of radius.
Citation
Sergei Ivanov. "On Gromov–Hausdorff stability in a boundary rigidity problem." Geom. Topol. 15 (2) 677 - 697, 2011. https://doi.org/10.2140/gt.2011.15.677
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