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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

Convex Hull Convex Body Large Root Small Triangle Unique Critical Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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