In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant widt...In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width,and the completion of the spherical regular simplexes are the most asymmetric bodies.展开更多
We introduce a family of measures（functions） of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As th...We introduce a family of measures（functions） of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As the mean Minkowski measures describe the symmetry of lower dimensional sections of a convex body, these new measures describe the symmetry of lower dimensional orthogonal projections.展开更多
基金Supported by the National Natural Science Foundation of China(12071334,12071277)。
文摘In this paper,we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width.Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width,and the completion of the spherical regular simplexes are the most asymmetric bodies.
基金The NSF(11401089)of Chinathe Science and Technology Project(20130101065JC)of Jilin Province
文摘We introduce a family of measures（functions） of asymmetry for convex bodies and discuss their properties. It turns out that this family of measures shares many nice properties with the mean Minkowski measures. As the mean Minkowski measures describe the symmetry of lower dimensional sections of a convex body, these new measures describe the symmetry of lower dimensional orthogonal projections.
