平面凸体的中间刺猬
The middle hedgehog of a planar convex body
摘要：
一个凸体的凸点是一个点的性质，即该物体和它在该点的反射的并集是凸的。证明了在平面上一个典型的凸体（在Baire范畴意义下）有无穷多个凸点。该证明利用了平面凸体$K$的“中刺猬”，它是由$K$的所有仿射直径的中点形成的曲线。所述结果由以下事实得出：对于典型的平面凸体，中间刺猬的凸包具有无穷多个暴露点。
英文摘要：
A convexity point of a convex body is a point with the property that the union of the body and its reflection in the point is convex. It is proved that in the plane a typical convex body (in the sense of Baire category) has infinitely many convexity points. The proof makes use of the `middle hedgehog' of a planar convex body $K$, which is the curve formed by the midpoints of all affine diameters of $K$. The stated result follows from the fact that for a typical planar convex body the convex hull of the middle hedgehog has infinitely many exposed points.
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。
