Irina Markina, "Hausdorff measure of the singular set of quasiregular maps on Carnot groups", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 413704, 18 pages, 2003. https://doi.org/10.1155/S0161171203212370
Hausdorff measure of the singular set of quasiregular maps on Carnot groups
Recently, the theory of quasiregular mappings on Carnot groups has been developed intensively. Let stand for the homogeneous dimension of a Carnot group and let be the index of the last vector space of the corresponding Lie algebra. We prove that the -dimensional Hausdorff measure of the image of the branch set of a quasiregular mapping on the Carnot group is positive. Some estimates of the local index of quasiregular mappings are also obtained.
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