Geodesic
Zonoids with an equatorial characterization
Applications of Mathematics, Tome 61 (2016) no. 4, pp. 413-422.

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It is known that a local equatorial characterization of zonoids does not exist. The question arises: Is there a subclass of zonoids admitting a local equatorial characterization. In this article a sufficient condition is found for a centrally symmetric convex body to be a zonoid. The condition has a local equatorial description. Using the condition one can define a subclass of zonoids admitting a local equatorial characterization. It is also proved that a convex body whose boundary is an ellipsoid belongs to the class.
DOI : 10.1007/s10492-016-0139-5
Classification : 52A15, 53C45, 53C65
Keywords: integral geometry; convex body; zonoid; support function 
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Aramyan, Rafik. Zonoids with an equatorial characterization. Applications of Mathematics, Tome 61 (2016) no. 4, pp. 413-422. doi : 10.1007/s10492-016-0139-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0139-5/

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