椭球的对偶体积唯一确定及矩问题
Unique determination of ellipsoids by their dual volumes and the moment problem
摘要：
Gusakova和Zaporozhets证明了$\mathbb R^n$中的椭球是由它们的Steiner多项式唯一确定的（直到等距）。彼得罗夫和塔拉索夫在《$\mathbb R^3$》中证实了这一猜想。在本文中，我们解决了对偶问题。我们表明，任何椭圆在$\mathbb{R}^n$中心的原点是唯一确定的（等距）由其对偶施泰纳多项式。为了证明这个结果，我们把它归结为一个矩问题。作为一个副产品，我们给出了一个替代的证明彼得罗夫和塔拉索夫的结果。
英文摘要：
Gusakova and Zaporozhets conjectured that ellipsoids in $\mathbb R^n$ are uniquely determined (up to an isometry) by their Steiner polynomials. Petrov and Tarasov confirmed this conjecture in $\mathbb R^3$. In this paper we solve the dual problem. We show that any ellipsoid in $\mathbb{R}^n$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
