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arXiv · 1503.01321

Marked length rigidity for Fuchsian buildings

David Constantine·Jean-François Lafont
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Abstract

We consider finite 2-complexes X that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT(-1) metrics on X which are piecewise hyperbolic and satisfy a natural non-singularity condition at vertices are marked length spectrum rigid within certain classes of negatively curved, piecewise Riemannian metrics on X. As a key step in our proof, we show that the marked length spectrum function for such metrics determines the volume of X.

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David Constantine, Jean-François Lafont. 2015-03-04. Marked length rigidity for Fuchsian buildings. https://doi.org/10.1017/etds.2018.12

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