Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces
Abstract: 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.
- Location
-
Deutsche Nationalbibliothek Frankfurt am Main
- Extent
-
Online-Ressource
- Language
-
Englisch
- Bibliographic citation
-
Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces ; volume:1 ; number:2013 ; year:2013 ; pages:232-254
Analysis and geometry in metric spaces ; 1, Heft 2013 (2013), 232-254
- Creator
-
Balogh, Zoltán M.
Tyson, Jeremy T.
Wildrick, Kevin
- DOI
-
10.2478/agms-2013-0005
- URN
-
urn:nbn:de:101:1-2024041116413525410258
- Rights
-
Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
-
14.08.2025, 10:51 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Balogh, Zoltán M.
- Tyson, Jeremy T.
- Wildrick, Kevin
Other Objects (12)
Mappings of finite distortion on metric surfaces
Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
Coupled coincidence points for two mappings in metric spaces and cone metric spaces
SOME REMARKS ON SOBOLEV AND BI-SOBOLEV MAPPINGS
Sobolev spaces
Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces
Fixed points of terminating mappings in partial metric spaces
Prime ends in metric spaces and quasiconformal-type mappings
Fixed points of multivalued mappings in partial metric spaces
Fixed points of asymptotically regular mappings in metric spaces
Set-valued mappings in partially ordered fuzzy metric spaces
Duality of moduli and quasiconformal mappings in metric spaces
Mappings of finite distortion on metric surfaces
Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
Coupled coincidence points for two mappings in metric spaces and cone metric spaces
SOME REMARKS ON SOBOLEV AND BI-SOBOLEV MAPPINGS
Sobolev spaces
Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces
Fixed points of terminating mappings in partial metric spaces
Prime ends in metric spaces and quasiconformal-type mappings
Fixed points of multivalued mappings in partial metric spaces
Fixed points of asymptotically regular mappings in metric spaces
Set-valued mappings in partially ordered fuzzy metric spaces
Duality of moduli and quasiconformal mappings in metric spaces
Mappings of finite distortion on metric surfaces
Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces
Coupled coincidence points for two mappings in metric spaces and cone metric spaces
SOME REMARKS ON SOBOLEV AND BI-SOBOLEV MAPPINGS
Sobolev spaces
Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces
Fixed points of terminating mappings in partial metric spaces
Prime ends in metric spaces and quasiconformal-type mappings
Fixed points of multivalued mappings in partial metric spaces
Fixed points of asymptotically regular mappings in metric spaces
Set-valued mappings in partially ordered fuzzy metric spaces