Reduced strictly convex plane figure is of constant width
A convex body \(K\subset R^ d\) is called reduced if for each convex body K'\(\subset K (K'\neq K)\) the width of K' is less than the width of K. In 1978 W. Heil posed the problem if each strictly convex reduced body is of constant width. For reduced convex bodies with smooth boundary this was proved by \textit{H. Groemer} [Monatsh. Math. 96, 29-39 (1983; Zbl 0513.52003)]. The author proves Heil's problem for \(d=2\). A solution of Heil's problem for all d is announced by \textit{J. Böhm} [Diskrete Geometrie, 3. Kolloq., Salzburg 1985, 49-51 (1985; Zbl 0587.52001)].
scientific article; zbMATH DE number 3940132