Mapping n Grid Points Onto a Square Forces an Arbitrarily Large Lipschitz Constant
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384835" target="_blank" >RIV/00216208:11320/18:10384835 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00039-018-0445-z" target="_blank" >https://doi.org/10.1007/s00039-018-0445-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00039-018-0445-z" target="_blank" >10.1007/s00039-018-0445-z</a>
Alternative languages
Result language
angličtina
Original language name
Mapping n Grid Points Onto a Square Forces an Arbitrarily Large Lipschitz Constant
Original language description
We prove that the regular square grid of points in the integer lattice cannot be recovered from an arbitrary n^2-element subset of Z^2 via a mapping with prescribed Lipschitz constant (independent of n). This answers negatively a question of Feige from 2002. Our resolution of Feige's question takes place largely in a continuous setting and is based on some new results for Lipschitz mappings falling into two broad areas of interest, which we study independently. Firstly the present work contains a detailed investigation of Lipschitz regular mappings on Euclidean spaces, with emphasis on their bilipschitz decomposability in a sense comparable to that of the well known result of Jones. Secondly, we build on work of Burago and Kleiner and McMullen on non-realisable densities. We verify the existence, and further prevalence, of strongly non-realisable densities inside spaces of continuous functions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ16-01602Y" target="_blank" >GJ16-01602Y: Topological and geometric approaches to classes of permutations and graph properties</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Geometric and Functional Analysis
ISSN
1016-443X
e-ISSN
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Volume of the periodical
28
Issue of the periodical within the volume
3
Country of publishing house
CH - SWITZERLAND
Number of pages
56
Pages from-to
589-644
UT code for WoS article
000435786000002
EID of the result in the Scopus database
2-s2.0-85045765989