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arXiv · 1209.3709

Marked length rigidity for one dimensional spaces

David Constantine·Jean-François Lafont
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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.

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David Constantine, Jean-François Lafont. 2012-09-17. Marked length rigidity for one dimensional spaces. https://doi.org/10.1142/s1793525319500250

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