Geometry & Topology

On Gromov–Hausdorff stability in a boundary rigidity problem

Sergei Ivanov

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732301

Digital Object Identifier
doi:10.2140/gt.2011.15.677

Mathematical Reviews number (MathSciNet)
MR2800362

Zentralblatt MATH identifier
1219.53043

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

Keywords
boundary distance rigidity Gromov–Hausdorff topology

Citation

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


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