Uniqueness of a three-dimensional ellipsoid with given intrinsic volumes (Q2209751)

In 2017, Anna Gusakova and Dmitry Zapoprozhets conjectured that an ellipsoid in \(\mathbb{R}^n\) is uniquely (up to rigid motions) determined by its intrinsic volumes. The authors prove this conjecture for \(n=3\). Specifically, it is shown that if the volume, surface area and mean width of two ellipsoids in \( \mathbb{R}^3 \) are the same, then the ellipsoids are congruent.