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

Mathematics

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

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

ASJC Scopus subject areas

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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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.

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DO - 10.1007/s000390050056

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JO - Geometric and Functional Analysis

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ER -

Separated nets in Euclidean space and Jacobians of biLipschitz maps

Abstract

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