Disk patterns, quasi-duality and the uniform bounded diameter conjecture

Yusheng Luo; Yongquan Zhang

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arXiv · 2408.10344

Disk patterns, quasi-duality and the uniform bounded diameter conjecture

Yusheng Luo·Yongquan Zhang

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Abstract

We show that the diameter of the image of the skinning map on the deformation space of an acylindrical reflection group is bounded by a constant depending only on the topological complexity of the components of its boundary, answering a conjecture of Minsky in the reflection group setting. This result can be interpreted as a uniform rigidity theorem for disk patterns. Our method also establishes a connection between the diameter of the skinning image and certain discrete extremal width on the Coxeter graph of the reflection group.

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Yusheng Luo, Yongquan Zhang. 2024-08-19. Disk patterns, quasi-duality and the uniform bounded diameter conjecture. https://arxiv.org/abs/2408.10344

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