论文标题
椭圆形通过双重卷和瞬间问题的独特确定
Unique determination of ellipsoids by their dual volumes and the moment problem
论文作者
论文摘要
Gusakova和Zaporozhets猜想$ \ Mathbb r^n $中的椭圆形是由其steiner多项式唯一确定的（直至等轴测图）。彼得罗夫和塔拉索夫在$ \ mathbb r^3 $中证实了这一猜想。在本文中，我们解决了双重问题。我们表明，以$ \ mathbb {r}^n $为中心的任何椭球均由其双施塔纳多项式唯一确定（直至等轴测图）。为了证明这一结果，我们将其减少到时刻问题。作为副产品，我们提供了彼得罗夫和塔拉索夫结果的替代证明。
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.
