Reconstruction of Convex Bodies from Projection Curvature Radius Function

Details Reconstruction of Convex Bodies from Projection Curvature Radius Function Reconstruction of Convex Bodies from Projection Curvature Radius Function

2005-01-27

arxiv.org/abs/math/0501488v1

Mathematics

Differential Geometry

14 pages, 0 figures

Scientific paper

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.

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