2025/107/1-2 (10)
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DOI: 10.5486/PMD.2025.10128
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pp. 173-186
On the area of ordinary hyperbolic reduced polygons
Authors:
Ádám Sagmeister 
Abstract:
A convex body $R$ in the hyperbolic plane is reduced if any convex body $K\subset R$ has a smaller minimal width than $R$. We examine the area of a family of hyperbolic reduced $n$-gons, and prove that, within this family, regular $n$-gons have maximal area.
Keywords: convex geometry, hyperbolic geometry, minimal width, thickness, reduced bodies, reduced polygons
Mathematics Subject Classification: 51M09, 51M10, 52A55