Sets of constant width appear as a curiosity in the context of finite-dimensional Euclidean spaces. These sets are convex bodies of such an space with the property that the distance between any two distinct parallel supporting hyperplanes is constant. The easiest example of a set of constant width which is not a ball is the so called Reuleaux triangle in the Euclidean plane. This is the intersection of three closed discs of radius r, whose centers are the vertices of an equilateral triangle of side length r.
The aim of this talk is to show how, once finite-dimensional Euclidean spaces are replaced by arbitrary Banach spaces, the resulting concept of set of constant width becomes interesting in relation with several questions on the geometry of Banach spaces, mainly in what concerns the L-M theory.
@article{urn:eudml:doc:39866,
title = {Infinite-dimensional sets of constant width and their applications.},
journal = {Extracta Mathematicae},
volume = {5},
year = {1990},
pages = {41-52},
zbl = {1147.46304},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39866}
}
Rodríguez Palacios, Angel. Infinite-dimensional sets of constant width and their applications.. Extracta Mathematicae, Tome 5 (1990) pp. 41-52. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39866/