Boundary rigidity of CAT(0) cube complexes

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 proof, we use the bijection between CAT(0) cube complexes and median graphs, and corner peelings of median graphs. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.