On the Vector Sum of Two Convex Sets in Space
Steven George Krantz, Harold R. Parks · Canadian Journal of Mathematics · 1991
In the paper [KIS2], C . Kiselman studied the boundary smoothness of the vector sum of two smoothly bounded convex sets A and B in . He discovered the startling fact that even when A and B have real analytic boundary the set A + B need not have boundary smoothness exceeding C 20/3 (this result is sharp). When A and B have C ∞ boundaries, then the smoothness of the sum set breaks down at the level C 5 (see [KIS2] for the various pathologies that arise).