New York Journal of Mathematics
Volume 5 (1999) 121-130


Nets Hawk Katz

On the Self Crossing Six Sided Figure Problem

Published: September 29, 1999
Keywords: Cauchy-Scwartz, Hexagons, Bilinear
Subject: 42B25

It was shown by Carbery, Christ, and Wright that any measurable set E in the unit square in R2 not containing the corners of a rectangle with area greater than λ has measure bounded by O(\sqrt{λlog(1/λ)}). We remove the log under the additional assumption that the set does not contain the corners of any axis-parallel, possibly self-crossing hexagon with unsigned area bigger than λ. Our proof may be viewed as a bilinearization of Carbery, Christ, and Wright's argument.


The author was supported by EPSRC GR/l10024

Author information

Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, IL, 60607-7045