Ressource pédagogique : Igor Belegradek - Smoothness of Minkowski sum and generic rotations

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I will discuss whether the Minkowski sum of two compact convex bodies can be made smoother by a generic rotation of one of them.  Here "generic" is understood in the sense of Baire category. The main result is a construction of an infinitely differentiable convex plane domain whose Minkowski sum with any generically rotated copy of itself is not five times differentiable.

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