Skip to content
DraconiticResearch
Search Sources API
189,105 studies31 sourcesUpdated 39 min ago
PreprintCC BY 4.0arXiv

Quasicircularity of the Zakeri Curve and Capture Component Boundaries

  • Yuming Fu
  • Weiwei Su
Open at sourcePDFDOICite

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.

Related

  1. Menger Curve and Non-Planar Boundaries in Quotients of Hyperbolic Groups
    Rafaela Ioannou
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Geometric Boundaries of the Frohmanian Symplectic Tether: Formal Tracking of the 2D Clock Test and Open Analytic Inputs for Fefferman Statement (B)
    Benjamin Frohman
    Zenodo (CERN European Organization for Nuclear Research)Peer-reviewedLicence not stated8 citedGeneral mathematicsOpenAlex
  3. Construction of log Calabi--Yau boundaries from int-amplified endomorphisms
    Shou Yoshikawa
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Full termination of MMP for klt pairs with big boundaries
    Kenta Hashizume
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Helly complexes are Hellyfications of their boundaries
    Martín Blufstein
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{fu2026quasicircularity,
  title = {{Quasicircularity of the Zakeri Curve and Capture Component Boundaries}},
  author = {Yuming Fu and Weiwei Su},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34225},
  eprint = {2610.34225},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34225},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quasicircularity of the Zakeri Curve and Capture Component Boundaries
AU  - Yuming Fu
AU  - Weiwei Su
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34225
UR  - https://arxiv.org/abs/2610.34225
AB  - 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.
ER  -