Hyperbolic polygons of minimal perimeter with given angles

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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 Schlenker (Trans Am Math Soc 359(5): 2155-2189, 2007). © 2011 Springer Science+Business Media B.V.
Original languageEnglish
Pages (from-to)165-170
JournalGeometriae Dedicata
Volume156
Issue number1
DOIs
Publication statusPublished - 1 Feb 2012

Keywords

  • De Sitter sphere
  • Hyperbolic polygon
  • Minimizing
  • Perimeter

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