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 -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, -cscK metrics.
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}
}
Comments
This is the published version of the article