Polar coordinates in Carnot groups
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 theory, specifically, fundamental solutions for the \(p-\)Laplace operators. As applications of this result, the authors obtain exact capacity estimates, representation formulas and an explicit sharp constant for the Moser-Trudinger inequality. Topological and measure-theoretic consequences for quasiregular mappings are also obtained.
scientific article; zbMATH DE number 1922564