紧致Hessian流形上Hesse-Koszul流的收敛性

IF 1.8 1区数学 Q1 MATHEMATICS, APPLIED

Annales De L Institut Henri Poincare-Analyse Non Lineaire Pub Date : 2023-10-16 DOI:10.4171/aihpc/68

Stéphane Puechmorel, Tat Dat Tô

{"title":"紧致Hessian流形上Hesse-Koszul流的收敛性","authors":"Stéphane Puechmorel, Tat Dat Tô","doi":"10.4171/aihpc/68","DOIUrl":null,"url":null,"abstract":"We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result for a twisted Hesse-Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse-Einstein metric by Cheng-Yau and Caffarelli-Viaclovsky as well as the real Calabi theorem by Cheng-Yau, Delano\\e and Caffarelli-Viaclovsky.","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Convergence of the Hesse–Koszul flow on compact Hessian manifolds\",\"authors\":\"Stéphane Puechmorel, Tat Dat Tô\",\"doi\":\"10.4171/aihpc/68\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result for a twisted Hesse-Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse-Einstein metric by Cheng-Yau and Caffarelli-Viaclovsky as well as the real Calabi theorem by Cheng-Yau, Delano\\\\e and Caffarelli-Viaclovsky.\",\"PeriodicalId\":55514,\"journal\":{\"name\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Henri Poincare-Analyse Non Lineaire\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/aihpc/68\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/aihpc/68","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 4

摘要

研究了紧化Hessian流形上hessia - koszul流的长时间特性。当第一个仿射陈氏类为负时，我们证明了流收敛于唯一的黑塞-爱因斯坦度量。我们还得到了任意紧化Hessian流形上的扭曲hessia - koszul流的收敛性结果。这些结果给出了Cheng-Yau和Caffarelli-Viaclovsky给出的唯一黑塞-爱因斯坦度量存在性的替代证明，以及Cheng-Yau、Delano\e和Caffarelli-Viaclovsky给出的真实卡拉比定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Convergence of the Hesse–Koszul flow on compact Hessian manifolds

We study the long time behavior of the Hesse-Koszul flow on compact Hessian manifolds. When the first affine Chern class is negative, we prove that the flow converges to the unique Hesse-Einstein metric. We also derive a convergence result for a twisted Hesse-Koszul flow on any compact Hessian manifold. These results give alternative proofs for the existence of the unique Hesse-Einstein metric by Cheng-Yau and Caffarelli-Viaclovsky as well as the real Calabi theorem by Cheng-Yau, Delano\e and Caffarelli-Viaclovsky.

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

Annales De L Institut Henri Poincare-Analyse Non Lineaire 数学-应用数学

CiteScore

4.10

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.