Year: 2026
Type: preprint
Abstract: We report on a Lean 4 formalization of Sullivan's No Wandering Domains theorem: every Fatou component of a rational self-map of the Riemann sphere of degree at least two is eventually periodic. The project formalizes the relevant background in normal families, the Montel-Carathéodory theorem, Julia and Fatou sets, local Sobolev regularity and Wirtinger derivatives, the Cauchy and Beurling transforms, the equivalence of analytic and geometric quasiconformality, and the measurable Riemann mapping theorem. This paper describes the translation of this mathematics into Lean, the proof architecture, the reusable components, and the autoformalization workflow.
Source: arXiv (Cornell University)
Authors: Li, Ziang, Luo, Yusheng
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213396502