On a functional equation related to a pair of hedgehogs with congruent projections

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Myroshnychenko, Sergii¹ 

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

关键词: Convex geometry;    Classical hedgehogs;   

DOI  :  10.1016/j.jmaa.2016.07.040

来源: Elsevier

【 摘 要 】

Hedgehogs are geometrical objects that describe the Minkowski differences of arbitrary convex bodies in the Euclidean space En. We prove that two hedgehogs in E-n, n >= 3, coincide up to a translation and a reflection in the origin, provided that their projections onto any two-dimensional plane are directly congruent and have no direct rigid motion symmetries. Our result is a consequence of a more general analytic statement about the solutions of a functional equation in which the support functions of hedgehogs are replaced with two arbitrary twice continuously differentiable functions on the unit sphere. Published by Elsevier Inc.

【 授权许可】

Free