On Gromov-Hausdorff stability in a boundary rigidity problem

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

2010-05-06

arxiv.org/abs/1005.1052v3

Geom. Topol. 15 (2011), no. 2, 677-697

Mathematics

Differential Geometry

16 pages, v3: added a preliminaries section

Scientific paper

10.2140/gt.2011.15.677

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 $C^1$-close to that of $D$. More generally, we prove the same result under the assumptions that the boundary distance function of $M$ is $C^0$-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.

Affiliated with

Also associated with

No associations

Rating

On Gromov-Hausdorff stability in a boundary rigidity problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Gromov-Hausdorff stability in a boundary rigidity problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Gromov-Hausdorff stability in a boundary rigidity problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-26740