Marked length rigidity for one dimensional spaces
Metric Geometry
2019-11-21 v1 Geometric Topology
Abstract
We prove that for compact, non-contractible, one dimensional geodesic spaces, a version of the marked length spectrum conjecture holds. For a compact one dimensional geodesic space X, we define a subspace Conv(X). When X is non-contractible, we show that X deformation retracts to Conv(X). If two such spaces X, Y have the same marked length spectrum, we prove that Conv(X) and Conv(Y) are isometric to each other.
Cite
@article{arxiv.1209.3709,
title = {Marked length rigidity for one dimensional spaces},
author = {David Constantine and Jean-François Lafont},
journal= {arXiv preprint arXiv:1209.3709},
year = {2019}
}
Comments
39 pages, 6 figures. Corrected and substantially expanded version of arXiv:math/0301309