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The solution of the Minkowski problem for open surfaces in Riemannian space

Bodrenko, Andrei I.

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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