Carnot group - Open Access .click

Mathematische Zeitschrift, 2002
In the present paper, the authors describe a procedure for constructing ``polar coordinates'' in a certain class of Carnot groups. They show that the given construction can be carried out in groups of Heisenberg type and they give explicit formulas for the polar coordinate decomposition in that setting. The construction makes use of nonlinear potential
Zoltán M. Balogh, Jeremy T. Tyson
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Subharmonic functions on Carnot groups

Mathematische Annalen, 2003
The authors develop a potential theory for \(\Delta_G\)-subharmonic functions in \(\mathbb{R}^N\), where \(\Delta_G\) is the sub-Laplacian in a Carnot group \(G\). The main results are analogues to Riesz representation and Poisson-Jensen formulas, Nevanlinna type theorems, and a characterization of the \(\Delta_G\)-Riesz measures of upper bounded ...
Ermanno Lanconelli, Andrea Bonfiglioli
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Quasiregular maps on Carnot groups

Journal of Geometric Analysis, 1997
The authors develop a theory of quasiregular maps in a sub-Riemannian geometry of two-step Carnot groups. An analytic definition for quasiregularity is suggested and it is shown that conconstant quasiregular maps are open and discrete maps on Carnot groups which are two-step nilpotent and of Heisenberg type. Some results which are known to be valid in \
Juha Heinonen +3 more
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