科研之友
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摘要
We show the existence of a non-injective uniformly quasiregular mapping acting on the one-point compactification of the Heisenberg group a%26quot;i(1) equipped with a sub-Riemannian metric. The corresponding statement for arbitrary quasiregular mappings acting on sphere was proven by Martin (Conform. Geom. Dyn. 1:24-27, 1997). Moreover, we construct uniformly quasiregular mappings on with large-dimensional branch sets. We prove that for any uniformly quasiregular map g on there exists a measurable CR structure mu which is equivariant under the semigroup I%26quot; generated by g. This is equivalent to the existence of an equivariant horizontal conformal structure.
- 出版日期2012-7
