Mappings with bounded distortion on Heisenberg groups (Q2773611)

The notion of the Heisenberg groups \(\mathbb H^n\) was introduced by \textit{A. Korányi} and \textit{H.~M.~Reimann} in [Invent. Math. 80, 309-338 (1985; Zbl 0567.30017)]. Previously, the author proved the following properties for mappings with bounded distortion on the 1-dimensional Heisenberg group \(\mathbb H^1\): the morphism property for solutions to associated subelliptic equations, the local Hölder continuity, almost everywhere differentiability in the sense of Pansu (see [\textit{P.~Pansu}, Ann. Math. (2) 129, No. 1, 1-60 (1989; Zbl 0678.53042)]), openness and discreteness of the mappings with bounded distortion, the Liouville theorem, the limit theorem for sequence of mappings with bounded distortion, the local homeomorphism theorem (see, for example, the author's papers [Sib. Math. J. 40, No. 4, 682-694 (1999)], [Sib. Math. J. 41, No. 1, 40-48 (2000; Zbl 0962.30008)], and [Sib. Math. J. 41, No. 2, 257-267 (2000)]).NEWLINENEWLINE In the article under review, the author obtains the same results for the multidimensional Heisenberg groups \(\mathbb H^n\). He uses the same methods which were developed by him for the 1-dimensional Heisenberg group \(\mathbb H^1\).