Author(s)

Rafik Aramyan^1,2

¹Russian-Armenian (Slavonic) University, Yerevan, Armenia.
²Institute of Mathematics Armenian Academy of Sciences, Yerevan, Armenia.

In this article, we study necessary and sufficient conditions for a function, defined on the space of flags to be the projection curvature radius function for a convex body. This type of inverse problems has been studied by Christoffel, Minkwoski for the case of mean and Gauss curvatures. We suggest an algorithm of reconstruction of a convex body from its projection curvature radius function by finding a representation for the support function of the body. We lead the problem to a system of differential equations of second order on the sphere and solve it applying a consistency method suggested by the author of the article.

Integral Geometry, Convex Body, Projection Curvature, Support Function

Aramyan, R. (2015) Reconstruction of Three Dimensional Convex Bodies from the Curvatures of Their Shadows. American Journal of Computational Mathematics, 5, 86-95. doi: 10.4236/ajcm.2015.52007.