|
||||
|
![[The NASA Astrophysics Data System]](christof2.files/image001.gif)
![[Proud supporter of the International Year of Astronomy]](christof2.files/image003.gif)
The
Christoffel problem and two analogs of the Minkowski problem in Riemannian
space
eprint arXiv:0709.0158
Author finds the solutions of the Christoffel problem for open and
closed surfaces in Riemannian space. The Christoffel problem is reduced to the
problem of construction the continuous G-deformations preserving the sum of
principal radii of curvature 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 following analogs of the
Minkowski problem for open and closed surfaces in Riemannian space are being
considered in this article: 1) the problem of construction the surface with
prescribed mean curvature and condition of G-deformation; 2) the problem of
construction the deformations preserving the area of each arbitrary region of
surface and condition of G-deformation.
Keywords: Mathematics - Differential Geometry, Mathematics - Analysis of
PDEs, 53C20, 53C21
![[SI logo]](christof2.files/image004.gif){kind=small}
![[NASA logo]](christof2.files/image006.jpg){kind=small}
The ADS is Operated by the Smithsonian Astrophysical Observatory under NASA Grant NNX09AB39G