Density not realizable as the Jacobian determinant of a bilipschitz map
Abstract
Are every two separated nets in the plane bilipschitz equivalent? In the late 1990s, Burago and Kleiner and, independently, McMullen resolved this beautiful question negatively. Both solutions are based on a construction of a density function that is not realizable as the Jacobian determinant of a bilipschitz map. McMullen's construction is simpler than the Burago-Kleiner one, and we provide a full proof of its nonrealizability, which has not been available in the literature.
Keywords
Cite
@article{arxiv.1404.5877,
title = {Density not realizable as the Jacobian determinant of a bilipschitz map},
author = {Vojtěch Kaluža},
journal= {arXiv preprint arXiv:1404.5877},
year = {2017}
}
Comments
15 pages, the proof section (section 3) was significantly extended, two parts left to intuitive reasoning before were described rigorously, a small error in a constant factor in the definition of Omega was corrected (influences only calculations at the end, not a validity of the result), 1 picture added