On a Heilbronn-type problem

Let F   be a convex figure with area |F||F| and let G(n,F)G(n,F) denote the smallest number such that from any n points of F   we can get G(n,F)G(n,F) triangles with areas less than or equal to |F|/4|F|/4. In this article, to generalize some results of Soifer, we will prove that for any triangle T  , G(5,T)=3G(5,T)=3; for any parallelogram P  , G(5,P)=2G(5,P)=2; for any convex figure F  , if S(F)=6S(F)=6, then G(6,F)=4G(6,F)=4.