## Uniformization of Cantor sets with bounded geometry

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- by Vyron Vellis PDF
- Conform. Geom. Dyn.
**25**(2021), 88-103 Request permission

## Abstract:

In this note we provide a quasisymmetric taming of uniformly perfect and uniformly disconnected sets that generalizes a result of MacManus [Rev. Mat. Iberoamericana 15 (1999), pp. 267–277] from 2 to higher dimensions. In particular, we show that a compact subset of $\mathbb {R}^n$ is uniformly perfect and uniformly disconnected if and only if it is ambiently quasiconformal to the standard Cantor set $\mathcal {C}$ in $\mathbb {R}^{n+1}$.## References

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## Additional Information

**Vyron Vellis**- Affiliation: Department of Mathematics, The University of Tennessee, Knoxville, Tennessee 37916
- MR Author ID: 1058764
- Email: vvellis@utk.edu
- Received by editor(s): January 24, 2021
- Received by editor(s) in revised form: May 17, 2021
- Published electronically: August 10, 2021
- Additional Notes: The author was partially supported by the Academy of Finland project 257482 and NSF DMS grant 1952510.
- © Copyright 2021 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**25**(2021), 88-103 - MSC (2020): Primary 30C65; Secondary 30L05
- DOI: https://doi.org/10.1090/ecgd/360
- MathSciNet review: 4298216