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The
solution of the Minkowski problem for open surfaces in Riemannian space
eprint arXiv:0708.3929
Author reduces the Minkowski problem to the problem of construction the
G-deformations preserving the product of principal curvatures for every point
of surface in Riemannian space. G-deformation transfers every normal vector of
surface in parallel along the path of the translation for each point of
surface. The continuous G-deformations preserving the product of principal
curvatures of surface with boundary are considered in this article. The
equations of deformations which are obtained in this paper reduce to the
nonlinear boundary-value problem. The method of construction continuous
G-deformations preserving the product of principal curvatures of surface with
boundary and its qualitative analysis are presented in this article
Keywords: Mathematics - Differential Geometry, Mathematics - Analysis of
PDEs, 53C21, 53C20
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