3 research outputs found
Upper bounds for Heilbronn's triangle problem in higher dimensions
We develop a new simple approach to prove upper bounds for generalizations of
the Heilbronn's triangle problem in higher dimensions. Among other things, we
show the following: for fixed , any subset of of size
contains:
- points which span a simplex of volume at most ,
- points whose convex hull has volume at most ,
- points which span a -dimensional simplex of volume
at most .Comment: 10 pages, a significant update with new result