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.
Geometric and spectral properties of locally tessellating planar graphs
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abstract
In this article, we derive bounds for values of the global geometry of locally tessellating planar graphs, namely, the Cheeger constant and exponential growth, in terms of combinatorial curvatures. We also discuss spectral implications for the Laplacians.
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2025 1verdicts
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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.