On fractal Peano curves
Abstract
It is proved that for every fractal continuous mapping F: I\to I^2 of the unit interval onto the unit square there is a pair of points x,y\in I, such that F(x)F(y)^2\ge 5xy.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404533
 Bibcode:
 2004math......4533S
 Keywords:

 Metric Geometry;
 Geometric Topology;
 28A80
 EPrint:
 11 pages, in Russian, to appear in Proc. Steklov Math. Inst