论文标题
Heilbronn三角问题的新界限
New bounds for the Heilbronn triangle problem
论文作者
论文摘要
利用压缩的几何形状中的想法，我们改善了Heilbronn三角问题的当前上和下限。特别是，通过让$δ（s）$表示单位光盘中$ s $点引起的三角形的最小区域，然后我们具有上限$$Δ（s）\ ll \ ll \ frac {1} {s^{s^{\ frac {\ frac {3} {3} {2}} {2}} {2} - ε}} $ $ $ $ $ $ $ $ $ $ $ $ - 和small ysly ysly small $ε：s： bound $δ（s）\ gg \ frac {\ log s} {s \ sqrt {s}}。$$
Using ideas from the geometry of compression, we improve on the current upper and lower bound of Heilbronn's triangle problem. In particular, by letting $Δ(s)$ denotes the minimal area of the triangle induced by $s$ points in a unit disc, then we have the upper bound $$Δ(s)\ll \frac{1}{s^{\frac{3}{2}-ε}}$$ for small $ε:=ε(s)>0$ and the lower bound$$Δ(s)\gg \frac{\log s}{s\sqrt{s}}.$$
