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Hyperbolic polygons of minimal perimeter with given angles. (English) Zbl 1236.51012
Author’s abstract: We prove that, among all convex hyperbolic polygons with given angles, the perimeter is minimized by the unique polygon with an inscribed circle. The proof relies on work of J.-M. Schlenker[Trans. Am. Math. Soc. 359, No. 5, 2155–2189 (2007; Zbl 1126.53041)].

MSC:
51M16 Inequalities and extremum problems in real or complex geometry
51M09 Elementary problems in hyperbolic and elliptic geometries
52A10 Convex sets in \(2\) dimensions (including convex curves)
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