NDLI: Quasiregular maps on Carnot groups

Content Provider	Springer Nature Link
Author	Heinen, Juha Holopainen, Ilkka
Copyright Year	1997
Abstract	In this paper we initiate the study of quasiregular maps in a sub-Riemannian geometry of general Carnot groups. We suggest an analytic definition for quasiregularity and then show that nonconstant quasiregular maps are open and discrete maps on Carnot groups which are two-step nilpotent and of Heisenberg type; we further establish, under the same assumption, that the branch set of a nonconstant quasiregular map has Haar measure zero and, consequently, that quasiregular maps are almost everywhere differentiable in the sense of Pansu. Our method is that of nonlinear potential theory. We have aimed at an exposition accessible to readers of varied background.
Starting Page	109
Ending Page	148
Page Count	40
File Format	PDF
ISSN	10506926
Journal	Journal of Geometric Analysis
Volume Number	7
Issue Number	1
e-ISSN	1559002X
Language	English
Publisher	Springer-Verlag
Publisher Date	1997-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quasiregular map Carnot group Heisenberg group nonlinear potential theory Quasiconformal mappings in ${\bf R}^n$, other generalizations Other generalizations Differential Geometry Convex and Discrete Geometry Fourier Analysis Abstract Harmonic Analysis Dynamical Systems and Ergodic Theory Global Analysis and Analysis on Manifolds
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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Quasiregular maps on Carnot groups