Frequency of Sobolev and quasiconformal dimension distortion

Balogh, Zoltan M.; Monti, Roberto; Tyson, Jeremy T. (2013). Frequency of Sobolev and quasiconformal dimension distortion. Journal de mathématiques pures et appliquées, 99(2), pp. 125-149. Gauthier-Villars 10.1016/j.matpur.2012.06.005

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We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Item Type:

Journal Article (Original Article)

Division/Institute:

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

UniBE Contributor:

Balogh, Zoltan; Monti, Roberto and Tyson, Jeremy

Subjects:

500 Science > 510 Mathematics

ISSN:

0021-7824

Publisher:

Gauthier-Villars

Language:

English

Submitter:

Mario Amrein

Date Deposited:

05 Jun 2014 14:29

Last Modified:

10 Dec 2014 15:48

Publisher DOI:

10.1016/j.matpur.2012.06.005

BORIS DOI:

10.7892/boris.41980

URI:

https://boris.unibe.ch/id/eprint/41980

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