Separated nets in Euclidean space and Jacobians of biLipschitz maps

Dmitri Burago; Bruce Kleiner

doi:10.1007/s000390050056

Separated nets in Euclidean space and Jacobians of biLipschitz maps

Dmitri Burago
, Bruce Kleiner

Research output: Contribution to journal › Article › peer-review

79 Scopus citations

Abstract

We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.

Original language	English (US)
Pages (from-to)	273-282
Number of pages	10
Journal	Geometric and Functional Analysis
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s000390050056
State	Published - 1998

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s000390050056

Cite this

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title = "Separated nets in Euclidean space and Jacobians of biLipschitz maps",

abstract = "We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.",

author = "Dmitri Burago and Bruce Kleiner",

note = "Funding Information: The rst author is supported by a Sloan Foundation Fellowship and NSF grant DMS-95-05175, and the second author is supported by a Sloan Foundation Fellowship and NSF grants DMS-95-05175 and DMS-96-26911.",

year = "1998",

doi = "10.1007/s000390050056",

language = "English (US)",

volume = "8",

pages = "273--282",

journal = "Geometric and Functional Analysis",

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publisher = "Springer International Publishing",

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T1 - Separated nets in Euclidean space and Jacobians of biLipschitz maps

AU - Burago, Dmitri

AU - Kleiner, Bruce

N1 - Funding Information: The rst author is supported by a Sloan Foundation Fellowship and NSF grant DMS-95-05175, and the second author is supported by a Sloan Foundation Fellowship and NSF grants DMS-95-05175 and DMS-96-26911.

PY - 1998

Y1 - 1998

N2 - We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.

AB - We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.

UR - https://www.scopus.com/pages/publications/0032222147

UR - https://www.scopus.com/pages/publications/0032222147#tab=citedBy

U2 - 10.1007/s000390050056

DO - 10.1007/s000390050056

M3 - Article

AN - SCOPUS:0032222147

SN - 1016-443X

VL - 8

SP - 273

EP - 282

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 2

ER -

Separated nets in Euclidean space and Jacobians of biLipschitz maps

Abstract

All Science Journal Classification (ASJC) codes

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