In this note, we prove that finite CAT(0) cube complexes can be reconstructed from their boundary distances (computed in their 1-skeleta). This result was conjectured by Haslegrave, Scott, Tamitegama, and Tan (2023). The reconstruction of a finite cell complex from the boundary distances is the discrete version of the boundary rigidity problem, which is a classical problem from Riemannian geometry. In the proofs, we use the bijection between CAT(0) cube complexes and median graphs and the corner peelings of median graphs.

翻译：本文证明了有限CAT(0)立方复形可由其边界距离（在其1-骨架中计算）重构。该结果由Haslegrave、Scott、Tamitegama及Tan（2023）提出猜想。通过边界距离重构有限胞复形是黎曼几何经典问题——边界刚性问题的离散版本。在证明过程中，我们利用了CAT(0)立方复形与中值图之间的双射关系，以及中值图的角剥离方法。