Unique determination of ellipsoids by their dual volumes and the moment problem

2020/07/16 by Sergii Myroshnychenko, Kateryna Tatarko, Myroshnychenko, Sergii +3 · 1 citation
Social Sciences · #52A20 #52A39 #FOS: Mathematics #Historical Geography and Cartography #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2007.08079

openalex publication_date 2020/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Gusakova and Zaporozhets conjectured that ellipsoids in \mathbb Rⁿ are uniquely determined (up to an isometry) by their Steiner polynomials. Petrov and Tarasov confirmed this conjecture in \mathbb R³. In this paper we solve the dual problem. We show that any ellipsoid in ℝⁿ centered at the origin is uniquely determined (up to an isometry) by its dual Steiner polynomial. To prove this result we reduce it to a problem of moments. As a by-product we give an alternative proof of the result of Petrov and Tarasov.

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