Mean Minkowski Measures Of Symmetry And Dual Mean Minkowski Measures Of Symmetry

As an analogy to mean Minkowski measures of symmetry introduced and studied by G. Toth, in this thesis we proposed a sort of geometric affine invariants for convex bodies, the dual mean Minkowski measures of symmetry, and we study some basic properties of these measures of symmetry as well.Contrast to the mean Minkowski measures of symmetry which provide information of lower dimensional sections of a convex body, characterizing how symmetric the sections are, the dual mean Minkowski measures of symmetry provide information of lower dimensional projections of a convex body, showing how symmetric the projections are.The main achievements in this thesis include the following1) The best upper and lower bounds of the dual mean Minkowski measures are given and the corresponding extremal convex bodies are found or characterized.2) Some equivalent definitions of support configuration are given; properties of support configurations are discussed.3) The sub-arithmeticity and super-additivity of the dual mean Minkowski measures of symmetry, which are crucial in studying dual mean Minkowski measures, are obtained.