Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Snowballs are quasiballs


Author: Daniel Meyer
Journal: Trans. Amer. Math. Soc. 362 (2010), 1247-1300
MSC (2000): Primary 30C65
DOI: https://doi.org/10.1090/S0002-9947-09-04635-2
Published electronically: October 5, 2009
MathSciNet review: 2563729
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce snowballs, which are compact sets in $ \mathbb{R}^3$ homeomorphic to the unit ball. They are $ 3$-dimensional analogs of domains in the plane bounded by snowflake curves. For each snowball $ \mathcal{B}$ a quasiconformal map $ f\colon \mathbb{R}^3\to \mathbb{R}^3$ is constructed that maps $ \mathcal{B}$ to the unit ball.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 30C65

Retrieve articles in all journals with MSC (2000): 30C65


Additional Information

Daniel Meyer
Affiliation: Department of Mathematics, University of Helsinki, P.O. Box 68, Gustaf Hällströmin katu 2b, FI-00014 University of Helsinki, Finland
Email: dmeyermail@gmail.com

DOI: https://doi.org/10.1090/S0002-9947-09-04635-2
Keywords: Quasiconformal maps, quasiconformal uniformization, snowball
Received by editor(s): August 16, 2007
Published electronically: October 5, 2009
Additional Notes: This research was partially supported by an NSF postdoctoral fellowship and by NSF grant DMS-0244421.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.