On the Existence of Weighted-cscK Metrics
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909904106684416 |
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| author | Han, Jiyuan Liu, Yaxiong |
| author_facet | Han, Jiyuan Liu, Yaxiong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Existence of Weighted-cscK Metrics Han, Jiyuan Liu, Yaxiong Differential Geometry Analysis of PDEs 53C55 (Primary) 53C21, 32J27, 58J60 (Secondary) 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. |
| title | On the Existence of Weighted-cscK Metrics |
| topic | Differential Geometry Analysis of PDEs 53C55 (Primary) 53C21, 32J27, 58J60 (Secondary) |
| url | https://arxiv.org/abs/2406.10939 |