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 -