On the Existence of Weighted-cscK Metrics
Jiyuan Han, Yaxiong Liu · arXiv (Cornell University) · 2024
In this paper, we prove that on a smooth Kähler manifold, the $\mathbb{G}$-coercivity of the weighted Mabuchi functional implies the existence of the (v, w)-weighted-cscK (extremal) metric with v log-concave (firstly studied in \cite{Lah19}), e.g, cscK metrics, Kähler-Ricci solitons, $μ$-cscK metrics.