{"title":"On the existence of weighted-cscK metrics","authors":"Jiyuan Han , Yaxiong Liu","doi":"10.1016/j.aim.2025.110125","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we prove that on a smooth Kähler manifold, the <span><math><mi>G</mi></math></span>-coercivity of the weighted Mabuchi functional implies the existence of the <span><math><mo>(</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>)</mo></math></span>-weighted-cscK (extremal) metric with v log-concave (firstly studied in <span><span>[33]</span></span>), e.g., extremal metrics, Kähler–Ricci solitons, <em>μ</em>-cscK metrics.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"463 ","pages":"Article 110125"},"PeriodicalIF":1.5000,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0001870825000234","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove that on a smooth Kähler manifold, the -coercivity of the weighted Mabuchi functional implies the existence of the -weighted-cscK (extremal) metric with v log-concave (firstly studied in [33]), e.g., extremal metrics, Kähler–Ricci solitons, μ-cscK metrics.
期刊介绍：
Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.
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