Best constants for Lipschitz quotient mappings in polygonal norms

Olga Maleva, Cristina Villanueva-Segovia

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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.
Original languageEnglish
Pages (from-to)116-144
Number of pages32
JournalMathematika
Volume67
Issue number1
Early online date23 Nov 2020
DOIs
Publication statusPublished - Jan 2021

Keywords

  • Lipschitz function
  • Lipschitz quotient mapping
  • Polygonal norm

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