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arXiv · 2610.34225

Quasicircularity of the Zakeri Curve and Capture Component Boundaries

Yuming Fu·Weiwei Su
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Abstract

For a fixed irrational rotation number of bounded type, we prove that the locus of critically marked cubic polynomials whose two critical points lie on the boundary of the fixed Siegel disk is a quasicircle. This locus is known as the Zakeri curve. The main step is a boundary correspondence lemma for holomorphic families of disks with uniformly quasiconformal extensions. We further prove that every capture component in this family is a quasidisk, including components attached to the Zakeri curve.

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Yuming Fu, Weiwei Su. 2026-10-25. Quasicircularity of the Zakeri Curve and Capture Component Boundaries. https://arxiv.org/abs/2610.34225

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