Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666983 | Advances in Mathematics | 2010 | 15 Pages |
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.
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