Geodesic
Closure of Classes of Mappings with Bounded Distortion on Carnot Groups
Matematičeskie trudy, Tome 5 (2002) no. 2, pp. 92-137

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It is known that the limit of a locally uniformly convergent sequence of analytic functions is an analytic function. Yu. G. Reshetnyak obtained a natural generalization of this result in the theory of mappings with bounded distortion: the limit of a locally uniformly convergent sequence of mappings with bounded distortion is a mapping with bounded distortion. The present article is devoted to extending this result to nonholonomic structures. As a model, we consider the geometry of Carnot groups. Since the geometry of these groups is non-Riemannian, there appear some constraints on applying analytic tools for groups. In particular, at present the method of the proof by Yu. G. Reshetnyak for the above-mentioned result cannot be implemented for Carnot groups. We give a method of proving the closure theorem which is new also for Euclidean space. 
@article{MT_2002_5_2_a2,
     author = {S. K. Vodop'yanov},
     title = {Closure of {Classes} of {Mappings} with {Bounded} {Distortion} on {Carnot} {Groups}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {92--137},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2002_5_2_a2/}
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S. K. Vodop'yanov. Closure of Classes of Mappings with Bounded Distortion on Carnot Groups. Matematičeskie trudy, Tome 5 (2002) no. 2, pp. 92-137. http://geodesic.mathdoc.fr/item/MT_2002_5_2_a2/