几类凸多边形区域单叶性内径的一些注记

Some Remarks on the Inner Radius of Univalency for Convex Polygons

根据Leila Miller-Van Wieren关于Nehari圆的判定定理,否定了关于长方形区域、等角六边形区域都是Nehari圆的猜测.并且得到边长比不超出一定范围的平行四边形区域的单叶性内径,同时证明了超出此范围的平行四边形区域不是Nehari圆.

By using a theorem of Leila MiUer-Van Wieren, we get a negative answer to the conjecture that the rect- angle domains and equiangular hexagons are always Nehari disk. We also get the inner radius of univalency of the parallelogrammic domains whose ratio of longer and shorter side does not exceed an upper bound. And we prove that the parallelogrammic domains are not Nehari disk when the ratio of longer and shorter side exceeds the bound.