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Conformally K\"{a}hler, Einstein-Maxwell metrics and $f$-extremal metrics aregeneralization of canonical metrics in K\"{a}hler geometry. We introduceuniform K-stability for toric K\"{a}hler manifolds, and show that uniformK-stability is necessary condition for the existence of $f$-extremal metrics ontoric manifolds. Furthermore, we show that uniform K-stability is equivalent toproperness of relative K-energy.

Uniform K-stability and Conformally K\"{a}hler, Einstein-Maxwell geometry on toric manifolds