Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

Balogh, Zoltán M.; Tyson, Jeremy T.; Wildrick, Kevin (2013). Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces. Analysis and Geometry in Metric Spaces, 1, pp. 232-254. Versita 10.2478/agms-2013-0005

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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 size of the set of leaves of the foliation that are mapped onto sets of higher dimension. We discuss key examples of such foliations, including foliations of the Heisenberg group by left and right cosets of horizontal subgroups.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan; Tyson, Jeremy and Wildrick, Kevin Michael

Subjects:

500 Science > 510 Mathematics

ISSN:

2299-3274

Publisher:

Versita

Language:

English

Submitter:

Mario Amrein

Date Deposited:

12 Mar 2014 11:57

Last Modified:

15 Jan 2015 16:56

Publisher DOI:

10.2478/agms-2013-0005

BORIS DOI:

10.7892/boris.41968

URI:

https://boris.unibe.ch/id/eprint/41968

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