Geodesic
On the Vector Sum of Two Convex Sets in Space
Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 347-355

Voir la notice de l'article provenant de la source Cambridge University Press

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). 
Krantz, Steven G.; Parks, Harold R. On the Vector Sum of Two Convex Sets in Space. Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 347-355. doi: 10.4153/CJM-1991-020-7
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