论文标题
同时发生的猜想的注释
A note on the concurrent normal conjecture
论文作者
论文摘要
从\ mathbb {r}^n $中的任何凸面$ k \ in \ mathbb {r}^n $中的任何凸面上都有一个猜测，在$ k $的内部中存在一个点，这些点属于$ k $的边界的不同点，至少属于$ 2N $正常。猜想以$ n = 2,3,4 $而众所周知。在最近的Y. Martinez-Maure的预印象的激励下，我们简短地证明了他的结果：对于尺寸$ n \ geq 3 $，在轻度条件下，几乎每个正常都通过边界到平稳的凸面$ k \ in \ mathbb {r}^n $包含至少6美元的$ 6 $ $ k $ y MATHBB {r}^n $。
It is conjectured since long that for any convex body $K \in \mathbb{R}^n$ there exists a point in the interior of $K$ which belongs to at least $2n$ normals from different points on the boundary of $K$. The conjecture is known to be true for $n=2,3,4$. Motivated by a recent preprint of Y. Martinez-Maure, we give a short proof of his result: for dimension $n\geq 3$, under mild conditions, almost every normal through a boundary point to a smooth convex body $K\in \mathbb{R}^n$ contains an intersection point of at least $6$ normals from different points on the boundary of $K$.
