2 papers
math.MG2026
A unified approach to Penner, Ptolemy, and Casey's theorems in several dimensions
Isabella Lewis, Ian Short
We prove Penner's theorem on horocycles and theorems of Ptolemy and Casey, all with full converses, in hyperbolic space of several dimensions. Recently Waddle observed that the equ…
math.CV2025
Iterated function systems of holomorphic maps
Marco Abate, Ian Short
We unify and advance a host of works on iterated function systems of holomorphic self-maps of hyperbolic Riemann surfaces. Our foremost result is a generalisation to left iterated…