We investigate the relation between the maximum cardinality N of the level sets of a Lipschitz quotient mapping of the plane and the ratio between its Lipschitz and co‐Lipschitz constants, with respect to the polygonal norms, and establish that bounds of $1/N$ previously shown to be sharp for Euclidean norm stay sharp for polygonal n‐norms if and only if n is not divisible by 4.

中文翻译：

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多边形范数中LIPSCHITZ商映射的最佳常数

我们针对多边形范数研究平面的Lipschitz商映射的水平集的最大基数N与它的Lipschitz和co-Lipschitz常数之间的比率之间的关系，并建立了$\mathrm{1个}/ñ$当且仅当n不能被4整除时，先前显示的对欧几里得范数才是锐利的，而对于多边形n范数则保持锐利。