Hyperbolic polygons of minimal perimeter in punctured discs
Geometric Topology
2016-09-28 v1
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.
Keywords
Cite
@article{arxiv.1609.08460,
title = {Hyperbolic polygons of minimal perimeter in punctured discs},
author = {Joan Porti},
journal= {arXiv preprint arXiv:1609.08460},
year = {2016}
}
Comments
12 pages