On a Heilbronn-type problem Original Research Article

Let F be a convex figure with area image and let image denote the smallest number such that from any n points of F we can get image triangles with areas less than or equal to image. In this article, to generalize some results of Soifer, we will prove that for any triangle T, image; for any parallelogram P, image; for any convex figure F, if image, then image.