Results 201 to 210 of about 14,687 (238)

Quasi-convex Functions in Carnot Groups*

Chinese Annals of Mathematics, Series B, 2007
The authors introduce the concept of \(h\)-quasiconvexity which generalizes the notion of \(h\)-convexity in the Carnot group \(G\). An example of \(h\)-quasiconvex function which is not \(h\)-convex is provided. Some interesting properties similar to those of \(h\)-convex functions on \(G\) are given.
Sun, Mingbao, Yang, Xiaoping
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Mikhlin’s problem on Carnot groups

Siberian Mathematical Journal, 2008
Summary: We consider one class of singular integral operators over the functions on domains of Carnot groups.
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Riemannian approximation in Carnot groups

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2021
We present self-contained proofs of the stability of the constants in the volume doubling property and the Poincaré and Sobolev inequalities for Riemannian approximations in Carnot groups. We use an explicit Riemannian approximation based on the Lie algebra structure that is suited for studying nonlinear subelliptic partial differential equations.
András Domokos, Juan J. Manfredi, Diego Ricciotti   +2 more
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Polar coordinates in Carnot groups

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
Balogh, Zoltán M., Tyson, Jeremy T.
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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 ...
Bonfiglioli, Andrea, Lanconelli, Ermanno
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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 \
Heinonen, Juha, Holopainen, Ilkka
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Breast Cancer Statistics, 2022

Ca-A Cancer Journal for Clinicians, 2022
Hyuna Sung, Kimberly D Miller, Rebecca L Siegel   +2 more
exaly  

Submanifolds in Carnot Groups

2008
The book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure; particular emphasis is given to the case of Heisenberg groups. A Geometric Measure Theory viewpoint is adopted, and features as intrinsic perimeters, Hausdorff measures, area formulae, calibrations and minimal surfaces are ...
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Convexity in Carnot groups

2005
We give an account of recent results and open questions related to the notion of convexity in Carnot groups.
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