Hyperbolic polygons of minimal perimeter in punctured discs

2016/09/27 by Joan Porti, Porti, Joan
Mathematics · #51M16 #57M20 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:51M16 #msc:57M20

paper · pdf · doi:10.48550/arxiv.1609.08460

12 pages

arxiv created 2016/09/27 · arxiv updated 2016/09/28

Abstract

We prove that, among the polygons in a punctured disc with fixed angles, the perimeter is minimized by the polygon with an inscribed horocycle centered at the puncture. We generalize this to a disc with a cone point and to an annulus with a geodesic boundary component and a complete end. Then we apply this result to describe the minimum of the spine systole on the moduli space of punctured surfaces.

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