Mapping n Grid Points Onto a Square Forces an Arbitrarily Large Lipschitz Constant

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Mapping n Grid Points Onto a Square Forces an Arbitrarily Large Lipschitz Constant

Popis výsledku v původním jazyce

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&apos;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.

Název v anglickém jazyce

Mapping n Grid Points Onto a Square Forces an Arbitrarily Large Lipschitz Constant

Popis výsledku anglicky

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&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ16-01602Y" target="_blank" >GJ16-01602Y: Topologické a geometrické přístupy k permutačním třídám a grafovým vlastnostem</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Geometric and Functional Analysis

ISSN

1016-443X

e-ISSN

—

Svazek periodika

28

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

56

Strana od-do

589-644

Kód UT WoS článku

000435786000002

EID výsledku v databázi Scopus

2-s2.0-85045765989