Tohoku Mathematical Journal
2022
March
SECOND SERIES VOL. 74, NO. 1

Tohoku Math. J.
74 (2022), 1-21

Title UNIFORM K-STABILITY AND CONFORMALLY KÄHLER, EINSTEIN-MAXWELL GEOMETRY ON TORIC MANIFOLDS

Author Yaxiong Liu

(Received May 6, 2020, revised September 28, 2020)
Abstract. Conformally Kähler, Einstein-Maxwell metrics and $f$-extremal metrics are generalization of canonical metrics in Kähler geometry. We introduce uniform K-stability for toric Kähler manifolds, and show that uniform K-stability is necessary condition for the existence of $f$-extremal metrics on toric manifolds. Furthermore, we show that uniform K-stability is equivalent to properness of relative K-energy.

Mathematics Subject Classification. Primary 53C25; Secondary 53C55.
Key words and phrases. cKEM metric, $f$-extremal metric, moment map, toric manifold, Uniform K-stability.

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