## Convex hulls of polynomial Julia sets

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- Proc. Amer. Math. Soc.
**149**(2021), 245-250 Request permission

## Abstract:

We prove P. Alexandersson’s conjecture that for every complex polynomial $p$ of degree $d \geq 2$ the convex hull $H_p$ of the Julia set $J_p$ of $p$ satisfies $p^{-1}(H_p) \subset H_p$. We further prove that the equality $p^{-1}(H_p) = H_p$ is achieved if and only if $p$ is affinely conjugated to the Chebyshev polynomial $T_d$ of degree $d$, to $-T_d$, or to a monomial $c z^d$ with $|c|=1$.## References

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## Additional Information

**Małgorzata Stawiska**- Affiliation: Mathematical Reviews, 416 Fourth Street, Ann Arbor, Michigan 48103
- ORCID: 0000-0001-5704-7270
- Email: stawiska@umich.edu
- Received by editor(s): April 29, 2020
- Published electronically: October 9, 2020
- Communicated by: Filippo Bracci
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**149**(2021), 245-250 - MSC (2010): Primary 37F10; Secondary 30C15, 52A10
- DOI: https://doi.org/10.1090/proc/15224
- MathSciNet review: 4172601