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Smoothness of vector sums of plane convex sets. (English) Zbl 0617.52004
The vector sum $$A+B$$ of two smooth convex sets A and B is not always infinitely smooth. For plane sets with real-analytic boundaries, the precise result is that the boundary of $$A+B$$ belongs to the Hölder class $$C^{20/3}$$. In the article smoothness classes are defined which are adapted to the calculation of vector sums of a finite number of convex sets in a two-dimensional vector space.

##### MSC:
 52A10 Convex sets in $$2$$ dimensions (including convex curves) 52A07 Convex sets in topological vector spaces (aspects of convex geometry) 26A16 Lipschitz (Hölder) classes
##### Keywords:
smoothness classes; plane convex sets
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