A priori bounds for some infinitely renormalizable quadratic: IV. Elephant Eyes
Abstract
In this paper we prove a priori bounds for an ``elephant eye'' combinatorics. Little $M$-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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Analytic and geometric function theory
Geometric and Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 29 January 2026
- Document type
- Preprint