Marked length rigidity for Fuchsian buildings
Marked length rigidity for Fuchsian buildings
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DOI：
10.1017/etds.2018.12
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发表时间：
2015-03
影响因子：
0.9
通讯作者：
D. Constantine;J.-F. Lafont
中科院分区：
文献类型：
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作者：
D. Constantine;J.-F. Lafont
我们考虑由组合自同构群的子群作为Fuchsian建筑商产生的有限$2$ -复合体$X$，我们假设这些子群自由而紧密地行动。我们证明了$X$上的局部CAT（$-1$）度量，它是分段双曲的，并且在顶点满足自然非奇异条件，在$X$上的某些负弯曲的，分段黎曼度量类中是标记长度谱刚性的。作为我们证明的关键一步，我们证明了这些度量的标记长度谱函数决定了X的体积。
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 $X$ .