复monge - ampantere方程的$L^\infty$估计

IF 5.7 1区数学 Q1 MATHEMATICS Annals of Mathematics Pub Date : 2021-06-04 DOI:10.4007/annals.2023.198.1.4

B. Guo, D. Phong, Freid Tong

{"title":"复monge - ampantere方程的$L^\\infty$估计","authors":"B. Guo, D. Phong, Freid Tong","doi":"10.4007/annals.2023.198.1.4","DOIUrl":null,"url":null,"abstract":"A PDE proof is provided for the sharp $L^\\infty$ estimates for the complex Monge-Amp\\`ere equation which had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.","PeriodicalId":8134,"journal":{"name":"Annals of Mathematics","volume":null,"pages":null},"PeriodicalIF":5.7000,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On $L^\\\\infty$ estimates for complex Monge-Ampère equations\",\"authors\":\"B. Guo, D. Phong, Freid Tong\",\"doi\":\"10.4007/annals.2023.198.1.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A PDE proof is provided for the sharp $L^\\\\infty$ estimates for the complex Monge-Amp\\\\`ere equation which had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.\",\"PeriodicalId\":8134,\"journal\":{\"name\":\"Annals of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":5.7000,\"publicationDate\":\"2021-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4007/annals.2023.198.1.4\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4007/annals.2023.198.1.4","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: 1

摘要

本文对复杂monge - ampante方程的精确$L^\infty$估计提供了偏微分方程证明，而这种估计以前需要多势理论。该证明涵盖了固定背景和退化背景度量两种情况。它扩展到更一般的满足结构条件的全非线性方程，并给出了Trudinger型的估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

On $L^\infty$ estimates for complex Monge-Ampère equations

A PDE proof is provided for the sharp $L^\infty$ estimates for the complex Monge-Amp\`ere equation which had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.

期刊最新文献

Parabolicity conjecture of $F$-isocrystals Erratum to "Disparity in Selmer ranks of quadratic twists of elliptic curves" Erratum to "On the averaged Colmez conjecture" A proof of the Erdős--Faber--Lovász conjecture Stable minimal hypersurfaces in ℝ^N+1+ℓ with singular set an arbitrary closed K⊂{0}×ℝ^ℓ