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Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

Zoltán M. Balogh, Jeremy T. Tyson, Kevin Wildrick (2013)

Analysis and Geometry in Metric Spaces

We quantify the extent to which a supercritical Sobolev mapping can increase the dimension of subsets of its domain, in the setting of metric measure spaces supporting a Poincaré inequality. We show that the set of mappings that distort the dimensions of sets by the maximum possible amount is a prevalent subset of the relevant function space. For foliations of a metric space X defined by a David–Semmes regular mapping Π : X → W, we quantitatively estimate, in terms of Hausdorff dimension in W, the...

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