Heilbronn Problem for Seven Points in a Planar Convex Body

  • Lu Yang
  • Zhenbing Zeng
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 4)

Abstract

Let K be a planar convex body (that means a compact convex set with non-empty interior), \K\ the area of K\ for any triangle ri7*27*3, by (rir2r3) denote its area; and let
$$\begin{array}{*{20}{c}} {({{r}_{1}}{{r}_{2}} \cdots {{r}_{n}}) : = \min \{ ({{r}_{i}}{{r}_{j}}{{r}_{k}})|1 \leqslant i < j < k \leqslant n\} ;} \hfill \\ {{{H}_{n}}(K) : = \frac{1}{{|K|}}\sup \{ ({{r}_{1}}{{r}_{2}} \cdots {{r}_{n}})|{{r}_{i}} \in K,i = 1, \cdots ,n\} .} \hfill \\ \end{array}$$

Keywords

Hull 

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Lu Yang
    • 1
  • Zhenbing Zeng
    • 1
  1. 1.Chengdu Institute of Computer ApplicationsAcademia SinicaChengduPeople’s Republic of China

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