Geometry & Topology

On Gromov–Hausdorff stability in a boundary rigidity problem

Sergei Ivanov

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Let M be a compact Riemannian manifold with boundary. We show that M is Gromov–Hausdorff close to a convex Euclidean region D of the same dimension if the boundary distance function of M is C1–close to that of D. More generally, we prove the same result under the assumptions that the boundary distance function of M is C0–close to that of D, the volumes of M and D are almost equal, and volumes of metric balls in M have a certain lower bound in terms of radius.

Article information

Geom. Topol., Volume 15, Number 2 (2011), 677-697.

Received: 27 July 2010
Revised: 24 January 2011
Accepted: 22 February 2011
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

boundary distance rigidity Gromov–Hausdorff topology


Ivanov, Sergei. On Gromov–Hausdorff stability in a boundary rigidity problem. Geom. Topol. 15 (2011), no. 2, 677--697. doi:10.2140/gt.2011.15.677.

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