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Quasi-convex Functions in Carnot Groups*
Chinese Annals of Mathematics, Series B, 2007The 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, 2008Summary: 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, 2021We 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 +2 more
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Polar coordinates in Carnot groups
Mathematische Zeitschrift, 2002In 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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