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• W2064022833 abstract "Lutwak, Yang and Zhang defined the cone volume functional U over convex polytopes in R n 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 R 2 and R 3 . Some new sharp inequalities characterizing parallelotopes in R n are established. Moreover, a simplified proof for the conjecture restricted to the class of origin-symmetric convex polytopes in R n is provided." @default.
• W2064022833 created "2016-06-24" @default.
• W2064022833 creator A5051711647 @default.
• W2064022833 date "2010-12-01" @default.
• W2064022833 modified "2023-09-29" @default.
• W2064022833 title "Extremum problems for the cone volume functional of convex polytopes" @default.
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• W2064022833 doi "https://doi.org/10.1016/j.aim.2010.05.016" @default.
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