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We determine the greatest lower bounds on the transverse Ricci curvature ofcompact toric Sasaki manifolds with positive basic first Chern class and withthe first Chern class of the contact bundle being trivial. This is based onWang-Zhu's and Futaki-Ono-Wang's works, and is an analogue of C. Li's work ontoric Fano manifolds.

Greatest lower bounds on the transverse Ricci curvature of some toric Sasaki manifolds