Title: BEST CONSTANTS FOR LIPSCHITZ QUOTIENT MAPPINGS IN POLYGONAL NORMS
Abstract: 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.