# The geometry of cyclic hyperbolic polygons

@article{Deblois2011TheGO,
title={The geometry of cyclic hyperbolic polygons},
author={J. Deblois},
journal={arXiv: Geometric Topology},
year={2011}
}
• J. Deblois
• Published 2011
• Mathematics
• arXiv: Geometric Topology
• A hyperbolic polygon is defined to be cyclic, horocyclic, or equidistant if its vertices lie on a metric circle, horocycle, or a component of the equidistant locus to a hyperbolic geodesic, respectively. Convex such $n$-gons are parametrized by the subspaces of $(0,\infty)^n$ that contain their side length collections, and area and circumcircle or "collar" radius determine symmetric, smooth functions on these spaces. We give formulas for and bounds on the derivatives of these functions, and… CONTINUE READING