On the Existence of Weighted-cscK Metrics
Abstract
In this paper, we prove that on a smooth K\"ahler manifold, the 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 Lah19), e.g, cscK metrics, K\"ahler-Ricci solitons, μ-cscK metrics.
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