Hausdorff Measure of the Singular Set of Quasiregular Maps on Carnot Groups
نویسنده
چکیده
Recently, the theory of quasiregular mappings on Carnot groups has been developed intensively. Let ν stand for the homogeneous dimension of a Carnot group and let m be the index of the last vector space of the corresponding Lie algebra. We prove that the (ν −m− 1)-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.
منابع مشابه
Singularities of quasiregular mappings on Carnot groups
In 1970 Poletskĭı applied the method of the module of a family of curves to describe behavior of quasiregular mappings (in another terminology mappings with bounded distortion) in Rn. In the present paper we generalize a result by Poletskĭı and study a singular set of a quasiregular mapping using the method of the module of a families of curves on Carnot groups.
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