On the closedness of classes of mappings with bounded distortion on Carnot groups. (Q1432607)

From the text (translated from the Russian): ``It is known that the limit of a locally uniformly converging sequence of analytic functions is an analytic function. \textit{Yu. G. Reshetnyak} [``Nauka'' Sib. Otdel., Novosibirsk (1982; Zbl 0487.30011)] obtained a natural generalization of this result in the theory of mappings with bounded distortion in Euclidean spaces: the limit of a locally uniformly converging sequence of mappings with bounded distortion is a mapping with bounded distortion. The proof of this result is based on a fundamental relation between the mappings and nonlinear potential theory, and also the weak discontinuity of Jacobians [op. cit.]. The present paper is devoted to the extension of this result to nonholonomic structures. As a model we consider the geometry of Carnot groups [\textit{P. Pansu}, Ann. of Math. (2) 129, No. 1, 1--60 (1989; Zbl 0678.53042)]. Since the geometry of these groups is not Riemannian, constraints arise in the applications of analytic techniques on groups. In particular, Reshetnyak's method for proving the above-mentioned result has not yet been realized on Carnot groups. The method of proof of the closedness theorem presented in this paper is new in the Euclidean space.''