On the Asymmetry for Convex Domains of Constant Width

Abstract

The extremal convex bodies of constant width for the Minkowski measure of asymmetry are discussed. A result, similar to that of H. Groemer's and of H. Lu's, is obtained, which states that, for the Minkowski measure of asymmetry, the most asymmetric convex domains of constant width in $\boldsymbol{R}^2$ are Reuleaux triangles.