Hyperbolic polygons of minimal perimeter in punctured discs

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Abstract

© 2018 Scuola Normale Superiore. All rights reserved. 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.
Original languageEnglish
Pages (from-to)831-844
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Volume18
Issue number3
Publication statusPublished - 1 Jan 2018

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