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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 $$X$$ .more » « less
