Article ID Journal Published Year Pages File Type
4666983 Advances in Mathematics 2010 15 Pages PDF
Abstract

Lutwak, Yang and Zhang defined the cone volume functional U over convex polytopes in Rn containing the origin in their interiors, and conjectured that the greatest lower bound on the ratio of this centro-affine invariant U to volume V is attained by parallelotopes. In this paper, we give affirmative answers to the conjecture in R2 and R3. Some new sharp inequalities characterizing parallelotopes in Rn are established. Moreover, a simplified proof for the conjecture restricted to the class of origin-symmetric convex polytopes in Rn is provided.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)