Best constants for Lipschitz quotient mappings in polygonal norms

Research output: Contribution to journalArticlepeer-review


Colleges, School and Institutes

External organisations

  • Facultad de Ciencias, UNAM, Mexico


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.


Original languageEnglish
Pages (from-to)116-144
Number of pages32
Issue number1
Early online date23 Nov 2020
Publication statusPublished - Jan 2021


  • Lipschitz function, Lipschitz quotient mapping, Polygonal norm