scholarly journals An estimate of the Hopf degree of fractional Sobolev mappings

2020 ◽  
Vol 148 (7) ◽  
pp. 2877-2891 ◽  
Author(s):  
Armin Schikorra ◽  
Jean Van Schaftingen
Keyword(s):  
Sobolev Mappings

scholarly journals Monotone Sobolev Mappings of Planar Domains and Surfaces

2015 ◽  
Vol 219 (1) ◽  
pp. 159-181 ◽  
Author(s):  
Tadeusz Iwaniec ◽  
Jani Onninen
Keyword(s):  
Planar Domains ◽  
Sobolev Mappings

Recent studies on Sobolev mappings

2017 ◽  
Vol 154 ◽  
pp. 25-42 ◽  
Author(s):  
Luigi D’Onofrio ◽  
Carlo Sbordone ◽  
Roberta Schiattarella
Keyword(s):  
Sobolev Mappings

scholarly journals Sobolev mappings with integrable dilatations

1993 ◽  
Vol 125 (1) ◽  
pp. 81-97 ◽  
Author(s):  
Juha Heinonen ◽  
Pekka Koskela
Keyword(s):  
Sobolev Mappings

Topology of Sobolev mappings III

2003 ◽  
Vol 56 (10) ◽  
pp. 1383-1415 ◽  
Author(s):  
Fengbo Hang ◽  
Fanghua Lin
Keyword(s):  
Sobolev Mappings

scholarly journals Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces

2013 ◽  
Vol 1 ◽  
pp. 232-254 ◽  
Author(s):  
Zoltán M. Balogh ◽  
Jeremy T. Tyson ◽  
Kevin Wildrick
Keyword(s):  
Hausdorff Dimension ◽  
Heisenberg Group ◽  
Metric Space ◽  
Metric Spaces ◽  
Higher Dimension ◽  
Metric Measure Spaces ◽  
Regular Mapping ◽  
Sobolev Mappings ◽  
Measure Spaces ◽  
Left And Right

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.

scholarly journals Lifting in compact covering spaces for fractional Sobolev mappings

2021 ◽  
Vol 14 (6) ◽  
pp. 1851-1871
Author(s):  
Petru Mironescu ◽  
Jean Van Schaftingen
Keyword(s):  
Covering Spaces ◽  
Sobolev Mappings
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