Marked length rigidity for Fuchsian buildings
arXiv:1503.01321 · doi:10.1017/etds.2018.12
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.
29 pages; this replaces an earlier version in which there was an error