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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.

52A10 Convex sets in \(2\) dimensions (including convex curves)
52A07 Convex sets in topological vector spaces (aspects of convex geometry)
26A16 Lipschitz (Hölder) classes
Full Text: DOI EuDML