Showing papers in "Siberian Mathematical Journal in 1995"

Hyperbolic volumes of Fibonacci manifolds

Abstract: A. Yu. Vesnin and A. D. Mednykh UDC 515.16 + 512.817.7 This article is devoted to the study of three-dimensional compact orientable hyperbolic manifolds connected with the Fibonacci groups. The Fibonacci groups F(2, m) = (Zl, z2,..., z,n : ziZi+l = zi+2, { mod m) were introduced by J. Conway [1]. The first natural question connected with these groups was whether they are finite or not [1]. It is known from [2-6] that the group F(2, m) is finite if and only if m = 1,2,3, 4,5, 7. Some algebraic generalizations of the groups

Analytic properties of quasiconformal mappings on Carnot groups

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

Stability of Classes of Affine Mappings

Abstract: Stability of classes of affine mappings is studied in the frameworks of A P Kopylov's ω-stability theory Various necessary and sufficient conditions for stability of these classes are obtained together with stability estimates in Sobolev norms over the whole domains