Covering functionals of cones and double cones

The least positive number γ such that a convex body K can be covered by m translates of γK is called the covering functional of K (with respect to m), and it is denoted by [Formula: see text] . Estimating covering functionals of convex bodies is an important part of Chuanming Zong’s quantitative pro...

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Detalles Bibliográficos
Autores principales: Wu, Senlin, Xu, Ke
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061585/
https://www.ncbi.nlm.nih.gov/pubmed/30137914
http://dx.doi.org/10.1186/s13660-018-1785-9
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author Wu, Senlin
Xu, Ke
author_facet Wu, Senlin
Xu, Ke
author_sort Wu, Senlin
collection PubMed
description The least positive number γ such that a convex body K can be covered by m translates of γK is called the covering functional of K (with respect to m), and it is denoted by [Formula: see text] . Estimating covering functionals of convex bodies is an important part of Chuanming Zong’s quantitative program for attacking Hadwiger’s covering conjecture. Estimations of covering functionals of cones and double cones, which are best possible for certain pairs of m and K, are presented.
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spelling pubmed-60615852018-08-09 Covering functionals of cones and double cones Wu, Senlin Xu, Ke J Inequal Appl Research The least positive number γ such that a convex body K can be covered by m translates of γK is called the covering functional of K (with respect to m), and it is denoted by [Formula: see text] . Estimating covering functionals of convex bodies is an important part of Chuanming Zong’s quantitative program for attacking Hadwiger’s covering conjecture. Estimations of covering functionals of cones and double cones, which are best possible for certain pairs of m and K, are presented. Springer International Publishing 2018-07-24 2018 /pmc/articles/PMC6061585/ /pubmed/30137914 http://dx.doi.org/10.1186/s13660-018-1785-9 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Wu, Senlin
Xu, Ke
Covering functionals of cones and double cones
title Covering functionals of cones and double cones
title_full Covering functionals of cones and double cones
title_fullStr Covering functionals of cones and double cones
title_full_unstemmed Covering functionals of cones and double cones
title_short Covering functionals of cones and double cones
title_sort covering functionals of cones and double cones
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061585/
https://www.ncbi.nlm.nih.gov/pubmed/30137914
http://dx.doi.org/10.1186/s13660-018-1785-9
work_keys_str_mv AT wusenlin coveringfunctionalsofconesanddoublecones
AT xuke coveringfunctionalsofconesanddoublecones

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