Rendiconti del Circolo Matematico di Palermo

, Volume 33, Issue 3, pp 436-440

First online:

Smooth approximation of convex bodies

  • Rolf SchneiderAffiliated withMathematisches Institut

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We describe a general approximation procedure for convex bodies which shows, in particular, that a body of constant width can be approximated, in the Hausdorff metric, by bodies of constant width with analytic boundaries (in fact, with algebraic support functions). Moreover, the approximating bodies have (at least) the same symmetries as the original one.