Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 61-72

QUASICONFORMAL MAPPINGS THAT HIGHLY DISTORT DIMENSIONS OF MANY PARALLEL LINES

Zoltán M. Balogh, Jeremy T. Tyson and Kevin Wildrick

Universität Bern, Mathematisches Institut
Sidlerstrasse 5, 3012 Bern, Switzerland; balogh.zoltan 'at' math.unibe.ch

University of Illinois at Urbana-Champaign, Department of Mathematics
1409 W Green Street, Urbana, IL 61801, U.S.A.; tyson 'at' math.uiuc.edu

Montana State University, Department of Mathematical Sciences
Wilson Hall, Bozeman, MT 59717, U.S.A.; kevin.wildrick 'at' montana.edu

Abstract. We construct a quasiconformal mapping of Rⁿ, n ≥ 2, that simultaneously distorts the Hausdorff dimension of a nearly maximal collection of parallel lines by a given amount. This answers a question of Balogh, Monti, and Tyson.

2010 Mathematics Subject Classification: Primary 30C65, 28A78; Secondary 46E35.

Key words: Sobolev mapping, quasiconformal mapping, foliation, dimension distortion.

Reference to this article: Z. M. Balogh, J. T. Tyson and K. Wildrick: Quasiconformal mappings that highly distort dimensions of many parallel lines. Ann. Acad. Sci. Fenn. Math. 42 (2017), 61-72.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4206