The Measure Of Asymmetry Of Convex Bodies

The main purpose of this thesis is to have a throughout research on the measure of asymmetry of convex bodies, which has attracted much attention of mathematicians for many years. We mainly discuss the Minkowski measure of asymmetry of convex bodies . With summarizing the historical development and the known results, we discover some results for convex domains of constant width.In Chap.I-III, the historic development and some known results are summarized and new proofs for some known theorems are given. In Chap.IV, the measure of asymmetry for convex domains of constant width is discussed, that Reuleaux triangles are the most asymmetric among all convex domains of constant width in terms of the Minkowski measure is proved first, then that the regular Reuleaux polygons are the most symmetric among all Reuleaux polygons with same orders is shown.