Hyperbolic polygons of minimal perimeter in punctured discs

Joan Porti

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arXiv · 1609.08460

Hyperbolic polygons of minimal perimeter in punctured discs

Joan Porti

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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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BibTeX RIS

Joan Porti. 2016-09-27. Hyperbolic polygons of minimal perimeter in punctured discs. https://arxiv.org/abs/1609.08460

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