MathDB

Let

D

be a convex subset of the

n

-dimensional space, and suppose that

D'

is obtained from

D

by applying a positive central dilatation and then a translation. Suppose also that the sum of the volumes of

D

and

D'

1

, and D \cap D'\not\equal{} \emptyset . Determine the supremum of the volume of the convex hull of

D \cup D'

taken for all such pairs of sets

D,D'

. L. Fejes-Toth, E. Makai

Problem Statement