Quasiconformal mappings that highly distort dimensions of many parallel lines

2016/01/26 by Balogh, Zoltán M., Tyson, Jeremy T., Wildrick, Kevin
#28A78 #30C65 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1601.07205

Abstract

We construct a quasiconformal mapping of n-dimensional Euclidean space, 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.

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