Hyperbolic polygons of minimal perimeter with given angles

2010/10/07 by Joan Porti, Porti, Joan
Mathematics · #51M09 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Mathematics and Applications #math.GT #msc:51M09

paper · pdf · doi:10.48550/arxiv.1010.1380

7 pages, 2 figures

arxiv created 2010/10/07 · openalex publication_date 2010/10/07 · arxiv updated 2010/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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