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On the Existence of Weighted-cscK Metrics

Differential Geometry 2025-11-18 v3 Analysis of PDEs

Abstract

In this paper, we prove that on a smooth K\"ahler manifold, the G\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, K\"ahler-Ricci solitons, μ\mu-cscK metrics.

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Cite

@article{arxiv.2406.10939,
  title  = {On the Existence of Weighted-cscK Metrics},
  author = {Jiyuan Han and Yaxiong Liu},
  journal= {arXiv preprint arXiv:2406.10939},
  year   = {2025}
}

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