About the Serpinsky-Knopp curve
arXiv:2003.01390 · doi:10.1070/RM9944
Abstract
The Serpinsky-Knopp curve is characterized as the only curve (up to isometry) that maps a unit segment onto a triangle of a unit area, so for any pair of points in the segment, the square of the distance between their images does not exceed four times the distance between them.
An abridged version of this article is accepted for publication in Russian Mathematical Surveys