Centroids and equilibrium points of convex bodies
arXiv:2407.19177
Abstract
The aim of this note is to survey the results in some geometric problems related to the centroids and the static equilibrium points of convex bodies. In particular, we collect results related to Grünbaum's inequality and the Busemann-Petty centroid inequality, describe classifications of convex bodies based on equilibrium points, and investigate the location and structure of equilibrium points, their number with respect to a general reference point as well as the static equilibrium properties of convex polyhedra.
27 pages, 1 table, 5 figures