paper

A priori bounds for some infinitely renormalizable quadratic: IV. Elephant Eyes

arXiv:2601.21905

Abstract

In this paper we prove a priori bounds for an ``elephant eye'' combinatorics. Little -copies specifying these combinatorics are allowed to converge to the cusp of the Mandelbrot set. To handle it, we develope a new geometric tool: uniform thin-thick decompositions for bordered Riemann surfaces.