© 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.
|Journal||Annali della Scuola normale superiore di Pisa - Classe di scienze|
|Publication status||Published - 1 Jan 2018|