On the Self Crossing Six Sided Figure Problem
Nets Hawk Katz · 1999
Abstract. 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 ( λ log 1). We remove the λ 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