A centerpoint theorem for three planar convex bodies

Hongyu Cheng, Amitabh Basu

For planar convex bodies $A_0,A_1,A_2$ satisfying $\frac{1}{2}(A_0+A_2)\subseteq A_1$, we prove that the union of the three slices $\{i\}\times A_i\subseteq {\mathbb{R}}^3$, $i=0,1,2$, co…