Abstract
ANALYTIC PROPERTIES OF QUASICONFORMAL MAPPINGS ON CARNOT GROUPS t) S. K. Vodop~yanov and A. V. Greshnov UDC 512.813.52+517.548.2+517.518.23 In a series of recent articles, the properties of nilpotent Lie groups and related objects have undergone intensive study in connection with various problems of sub-Riemannian geometry, analysis, and subel- liptic differential equations. The analytic questions in such problems are primarily connected with the presence of nontrivial commutation relations which, as a rule, prohibit straightforward translation of the technique developed for similar problems in Euclidean space. Such difficulties appear, for instance, in the problem concerning the differential properties of quasiconformal mappings on Carnot groups which is studied in the present article. A metric definition of a quasiconformal mapping can be given in an arbitrary metric space (see, for instance, [1]). However, for developing the theory of quasiconfor- mal mappings, in particular for establishing their analytic properties, the domain of definition must possess some extra structure. One of the fundamental results of the theory in the Euclidean space I~ n, n > 2, is the prop- erty of a quasiconformal mapping being absolutely continuous along almost all lines parallel to the coordinate axes (the
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