Mappings with convex potentials and the quasiconformal Jacobian problem

Leonid V. Kovalev; Diego Maldonado

doi:10.1215/ijm/1258138126

Mappings with convex potentials and the quasiconformal Jacobian problem

Leonid V. Kovalev, Diego Maldonado

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

20 Scopus citations

Abstract

This paper concerns convex functions that arise as potentials of quasiconformal mappings. Several equivalent definitions for such functions are given. We use them to construct quasiconformal mappings whose Jacobian determinants are singular on a prescribed set of Hausdorff dimension less than 1.

Original language	English (US)
Pages (from-to)	1039-1060
Number of pages	22
Journal	Illinois Journal of Mathematics
Volume	49
Issue number	4
DOIs	https://doi.org/10.1215/ijm/1258138126
State	Published - 2005
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1215/ijm/1258138126

Cite this

@article{c57c45d55e48406b8098233eab1cbb39,

title = "Mappings with convex potentials and the quasiconformal Jacobian problem",

abstract = "This paper concerns convex functions that arise as potentials of quasiconformal mappings. Several equivalent definitions for such functions are given. We use them to construct quasiconformal mappings whose Jacobian determinants are singular on a prescribed set of Hausdorff dimension less than 1.",

author = "Kovalev, {Leonid V.} and Diego Maldonado",

year = "2005",

doi = "10.1215/ijm/1258138126",

language = "English (US)",

volume = "49",

pages = "1039--1060",

journal = "Illinois Journal of Mathematics",

issn = "0019-2082",

publisher = "Duke University Press",

number = "4",

}

TY - JOUR

T1 - Mappings with convex potentials and the quasiconformal Jacobian problem

AU - Kovalev, Leonid V.

AU - Maldonado, Diego

PY - 2005

Y1 - 2005

N2 - This paper concerns convex functions that arise as potentials of quasiconformal mappings. Several equivalent definitions for such functions are given. We use them to construct quasiconformal mappings whose Jacobian determinants are singular on a prescribed set of Hausdorff dimension less than 1.

AB - This paper concerns convex functions that arise as potentials of quasiconformal mappings. Several equivalent definitions for such functions are given. We use them to construct quasiconformal mappings whose Jacobian determinants are singular on a prescribed set of Hausdorff dimension less than 1.

UR - http://www.scopus.com/inward/record.url?scp=33745321723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745321723&partnerID=8YFLogxK

U2 - 10.1215/ijm/1258138126

DO - 10.1215/ijm/1258138126

M3 - Article

AN - SCOPUS:33745321723

SN - 0019-2082

VL - 49

SP - 1039

EP - 1060

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 4

ER -

Mappings with convex potentials and the quasiconformal Jacobian problem

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this