Abstract
The existence and uniqueness of a surface with given geometric characteristics is one of the important topical problems of global differential geometry. By stating this problem in terms of analysis, we arrive at second-order elliptic and parabolic partial differential equations. In the present paper we consider generalized solutions of the Monge-Ampere equation ¦¦z ij ¦¦ = ϕ(x, z, p) in Λ n , wherez = z(x 1,...,z n ) is a convex function,p = (p 1,...,P n) = (∂z/∂x 1,...,ϖz/ϖx n), andz ij =ϖ 2 z/ϖx i ϖx j. We consider the Cayley-Klein model of the space Λ n and use a method based on fixed point principle for Banach spaces.
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