Reconstruction of Convex Bodies from Projection Curvature Radius Function

2005/01/27 by Aramyan Rafik, Rafik, Aramyan
Engineering · Mathematics · #52A20 #53C45 #Aerospace Engineering and Control Systems #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.math/0501488

openalex publication_date 2005/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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