It is shown by Makai, Martini, and \'Odor that a convex body$K\subset\mathbb{R}^n$, all of whose maximal sections pass through the origin,must be origin-symmetric. We prove a stability version of this result. We alsodiscuss a theorem of Koldobsky and Shane about determination of convex bodiesby fractional derivatives of the parallel section function, and establish thecorresponding stability result.
展开▼
机译：由Makai，Martini和\'Odor显示，凸体$ K \ subset \ mathbb {R} ^ n $（其所有最大截面均通过原点）必须是原点对称的。我们证明了该结果的稳定性。我们还讨论了用平行截面函数的分数导数确定凸体的Koldobsky和Shane定理，并建立了相应的稳定性结果。
展开▼
