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Smooth approximation of convex bodies

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Abstract

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.

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Authors and Affiliations

  1. Mathematisches Institut, Albertstr. 23 b, D-7800, Freiburg i. Br.

    Rolf Schneider

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  1. Rolf Schneider
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Schneider, R. Smooth approximation of convex bodies. Rend. Circ. Mat. Palermo 33, 436–440 (1984). https://doi.org/10.1007/BF02844505

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  • DOI: https://doi.org/10.1007/BF02844505

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