PreprintarXiv licencearXiv
Rigidity of Simple Parabolic Maps
Abstract
We prove that two simple parabolic rational maps with conformally conjugate completely invariant parabolic Fatou domains are globally conformally conjugate. The proof combines quasiconformal rigidity with the absence of invariant line fields for simple parabolic maps. Together with our previous existence theorem, the rigidity result gives existence and uniqueness of simple parabolic models for infinitely-connected fixed parabolic Fatou domains. We further obtain a rational-map analogue of the Goldberg--Milnor perturbation conjecture.
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BibTeX
@misc{gao2026rigidity,
title = {{Rigidity of Simple Parabolic Maps}},
author = {Ning Gao and Yan Gao and Wenjuan Peng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.22328},
eprint = {2608.22328},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22328},
}
RIS
TY - UNPB
TI - Rigidity of Simple Parabolic Maps
AU - Ning Gao
AU - Yan Gao
AU - Wenjuan Peng
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2608.22328
UR - https://arxiv.org/abs/2608.22328
AB - We prove that two simple parabolic rational maps with conformally conjugate completely invariant parabolic Fatou domains are globally conformally conjugate. The proof combines quasiconformal rigidity with the absence of invariant line fields for simple parabolic maps. Together with our previous existence theorem, the rigidity result gives existence and uniqueness of simple parabolic models for infinitely-connected fixed parabolic Fatou domains. We further obtain a rational-map analogue of the Goldberg--Milnor perturbation conjecture.
ER -