Geodesic
Approximation of Bodies of Constant Width and Reduced Bodies in a Normed Plane
Journal of convex analysis, Tome 19 (2012) no. 3, pp. 865-874

Voir la notice de l'article provenant de la source Heldermann Verlag

We prove that for every ε > 0 and for every convex body of constant width in a normed plane there exists a convex body of the same constant width whose boundary consists only of arcs of circles in the sense of the norm such that the Hausdorff distance between the two bodies is at most ε. This generalizes the Euclidean case proved by Blaschke. We also present a more general theorem about approximation of reduced bodies.
Classification : 52A10, 52A21, 52A27, 46B25
Mots-clés : Reduced convex body, body of constant width, normed plane, Hausdorff distance, approximation 
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     author = {M. Lassak},
     title = {Approximation of {Bodies} of {Constant} {Width} and {Reduced} {Bodies} in a {Normed} {Plane}},
     journal = {Journal of convex analysis},
     pages = {865--874},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a12/}
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M. Lassak. Approximation of Bodies of Constant Width and Reduced Bodies in a Normed Plane. Journal of convex analysis, Tome 19 (2012) no. 3, pp. 865-874. http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a12/