Best constants for Lipschitz quotient mappings in polygonal norms

Olga Maleva; Cristina Villanueva-Segovia

doi:10.1112/mtk.12064

Best constants for Lipschitz quotient mappings in polygonal norms

Olga Maleva, Cristina Villanueva-Segovia

Mathematics

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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 language	English
Pages (from-to)	116-144
Number of pages	32
Journal	Mathematika
Volume	67
Issue number	1
Early online date	23 Nov 2020
DOIs	https://doi.org/10.1112/mtk.12064
Publication status	Published - Jan 2021

Keywords

Lipschitz function
Lipschitz quotient mapping
Polygonal norm

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10.1112/mtk.12064Licence: Creative Commons: Attribution (CC BY)

Maleva_Villanueva‐Segovia_2020_Best_constants_for_Lipschitz_quotient_MathematikaFinal published version, 348 KBLicence: Creative Commons: Attribution (CC BY)

Differentiability and Small sets
Maleva, O. (Principal Investigator)
Engineering & Physical Science Research Council
1/07/16 → 30/06/19
Project: Research Councils

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KW - Polygonal norm

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Best constants for Lipschitz quotient mappings in polygonal norms

Abstract

Keywords

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Differentiability and Small sets

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