{"title":"A quantization proof of the uniform Yau–Tian–Donaldson conjecture","authors":"Kewei Zhang","doi":"10.4171/jems/1373","DOIUrl":null,"url":null,"abstract":"Using quantization techniques, we show that the $\\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence of twisted K\\\"ahler-Einstein metrics with arbitrary polarizations. Our approach mainly uses pluripotential theory, which does not involve Cheeger-Colding-Tian theory or the non-Archimedean language. A new computable criterion for the existence of constant scalar curvature K\\\"ahler metrics is also given.","PeriodicalId":50003,"journal":{"name":"Journal of the European Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2021-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the European Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/jems/1373","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: 21
Abstract
Using quantization techniques, we show that the $\delta$-invariant of Fujita-Odaka coincides with the optimal exponent in certain Moser-Trudinger type inequality. Consequently we obtain a uniform Yau-Tian-Donaldson theorem for the existence of twisted K\"ahler-Einstein metrics with arbitrary polarizations. Our approach mainly uses pluripotential theory, which does not involve Cheeger-Colding-Tian theory or the non-Archimedean language. A new computable criterion for the existence of constant scalar curvature K\"ahler metrics is also given.
期刊介绍:
The Journal of the European Mathematical Society (JEMS) is the official journal of the EMS.
The Society, founded in 1990, works at promoting joint scientific efforts between the many different structures that characterize European mathematics. JEMS will publish research articles in all active areas of pure and applied mathematics. These will be selected by a distinguished, international board of editors for their outstanding quality and interest, according to the highest international standards.
Occasionally, substantial survey papers on topics of exceptional interest will also be published. Starting in 1999, the Journal was published by Springer-Verlag until the end of 2003. Since 2004 it is published by the EMS Publishing House. The first Editor-in-Chief of the Journal was J. Jost, succeeded by H. Brezis in 2004.
The Journal of the European Mathematical Society is covered in:
Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.