Open Access
2011 On Gromov–Hausdorff stability in a boundary rigidity problem
Sergei Ivanov
Geom. Topol. 15(2): 677-697 (2011). DOI: 10.2140/gt.2011.15.677

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.

Citation

Download 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

Information

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

zbMATH: 1219.53043
MathSciNet: MR2800362
Digital Object Identifier: 10.2140/gt.2011.15.677

Subjects:
Primary: 53C23

Keywords: boundary distance rigidity , Gromov–Hausdorff topology

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.15 • No. 2 • 2011
MSP
Back to Top