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Solution of Laczkovich's Lipschitz mapping problem
Abstract
In 1991, Laczkovich asked whether every measurable set of positive measure in ℝd can be mapped onto a cube with a Lipschitz map. We show that the answer is positive for every d. Our results also give a positive answer for Kolmogorov's problem on contractions onto polygons with small measure loss in the case of Jordan measurable sets.
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BibTeX
@misc{gaspar2026solution,
title = {{Solution of Laczkovich's Lipschitz mapping problem}},
author = {Attila Gáspár},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38834},
eprint = {2610.38834},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38834},
}
RIS
TY - UNPB
TI - Solution of Laczkovich's Lipschitz mapping problem
AU - Attila Gáspár
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38834
UR - https://arxiv.org/abs/2610.38834
AB - In 1991, Laczkovich asked whether every measurable set of positive measure in ℝ^d can be mapped onto a cube with a Lipschitz map. We show that the answer is positive for every d. Our results also give a positive answer for Kolmogorov's problem on contractions onto polygons with small measure loss in the case of Jordan measurable sets.
ER -