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
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 
@article{JCA_2012_19_3_JCA_2012_19_3_a12,
     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},
     year = {2012},
     volume = {19},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a12/}
}
TY  - JOUR
AU  - M. Lassak
TI  - Approximation of Bodies of Constant Width and Reduced Bodies in a Normed Plane
JO  - Journal of convex analysis
PY  - 2012
SP  - 865
EP  - 874
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a12/
ID  - JCA_2012_19_3_JCA_2012_19_3_a12
ER  - 
%0 Journal Article
%A M. Lassak
%T Approximation of Bodies of Constant Width and Reduced Bodies in a Normed Plane
%J Journal of convex analysis
%D 2012
%P 865-874
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a12/
%F JCA_2012_19_3_JCA_2012_19_3_a12
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/