On the Uniqueness of Gravitational Centre |
| |
Authors: | Irmina Herburt |
| |
Affiliation: | (1) Department of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland |
| |
Abstract: | The dual volume of order α of a convex body A in R n is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R3 coincides with the maximizer of dual volume of order 2, thus it is unique. |
| |
Keywords: | Gravitational centre Gravitational potential Convex body Dual volume Radial centre |
本文献已被 SpringerLink 等数据库收录! |