On lower estimations of square-linear ratio for plane Peano curves
arXiv:2103.02478
Abstract
It is proved that for any mapping of a unit segment to a unit square, there is a pair of points of the segment for which the square of the Euclidean distance between their images exceeds the distance between them on the segment by at least times. And the additional condition that the images of the beginning and end of the segment belong to opposite sides of the square increases the estimate to .
3 figures