Abstract
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.
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Aramyan, R. Zonoids with an equatorial characterization. Appl Math 61, 413–422 (2016). https://doi.org/10.1007/s10492-016-0139-5
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DOI: https://doi.org/10.1007/s10492-016-0139-5