Finite minimal-perimeter shapes in hyperbolic {p,q} lattices are characterized; layer-constructed balls realize the Häggström-Jonasson-Lyons isoperimetric constant exactly for any vertex count.
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On minimal shapes and isoperimetric constants in hyperbolic lattices
Finite minimal-perimeter shapes in hyperbolic {p,q} lattices are characterized; layer-constructed balls realize the Häggström-Jonasson-Lyons isoperimetric constant exactly for any vertex count.