Geometry & Topology
- Geom. Topol.
- Volume 15, Number 2 (2011), 677-697.
On Gromov–Hausdorff stability in a boundary rigidity problem
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.
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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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. https://projecteuclid.org/euclid.gt/1513732301