Standard

On Gromov-Hausdorff stability in a boundary rigidity problem. / Ivanov, Sergei.

In: Geometry and Topology, Vol. 15, No. 2, 30.05.2011, p. 677-697.

Research output: Contribution to journal › Article › peer-review

Harvard

Ivanov, S 2011, 'On Gromov-Hausdorff stability in a boundary rigidity problem', Geometry and Topology, vol. 15, no. 2, pp. 677-697. https://doi.org/10.2140/gt.2011.15.677

APA

Ivanov, S. (2011). On Gromov-Hausdorff stability in a boundary rigidity problem. Geometry and Topology, 15(2), 677-697. https://doi.org/10.2140/gt.2011.15.677

Vancouver

Ivanov S. On Gromov-Hausdorff stability in a boundary rigidity problem. Geometry and Topology. 2011 May 30;15(2):677-697. https://doi.org/10.2140/gt.2011.15.677

Author

Ivanov, Sergei. / On Gromov-Hausdorff stability in a boundary rigidity problem. In: Geometry and Topology. 2011 ; Vol. 15, No. 2. pp. 677-697.

BibTeX

@article{0b2a680ba2484f919822859e31ffec09,
title = "On Gromov-Hausdorff stability in a boundary rigidity problem",
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.",
keywords = "53C23",
author = "Sergei Ivanov",
year = "2011",
month = may,
day = "30",
doi = "10.2140/gt.2011.15.677",
language = "English",
volume = "15",
pages = "677--697",
journal = "Geometry and Topology",
issn = "1465-3060",
publisher = "University of Warwick",
number = "2",

}

RIS

TY - JOUR

T1 - On Gromov-Hausdorff stability in a boundary rigidity problem

AU - Ivanov, Sergei

PY - 2011/5/30

Y1 - 2011/5/30

N2 - 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.

AB - 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.

KW - 53C23

UR - http://www.scopus.com/inward/record.url?scp=79957505834&partnerID=8YFLogxK

U2 - 10.2140/gt.2011.15.677

DO - 10.2140/gt.2011.15.677

M3 - Article

AN - SCOPUS:79957505834

VL - 15

SP - 677

EP - 697

JO - Geometry and Topology

JF - Geometry and Topology

SN - 1465-3060

IS - 2

ER -

ID: 49983834