Reconstruction of Convex Bodies from Projection Curvature Radius Function
arXiv:math/0501488
Abstract
In this article we pose the problem of existence and uniqueness of convex body for which the projection curvature radius function coincides with given function. We find a necessary and sufficient condition that ensures a positive answer to both questions and suggest an algorithm of construction of the body. Also we find a representation of the support function of a convex body by projection curvature radii.
arXiv comment14 pages, 0 figures