拉普拉斯G2流下的曲率捏缩估计

IF 1.6 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-09-17 DOI:10.1016/j.jfa.2025.111199

Chuanhuan Li , Yi Li

{"title":"拉普拉斯G2流下的曲率捏缩估计","authors":"Chuanhuan Li , Yi Li","doi":"10.1016/j.jfa.2025.111199","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we derive a pinching estimate for the traceless Ricci curvature in terms of scalar curvature and the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor under the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow for closed <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> structures. Then we apply this estimate to study the long time existence of the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow and prove that the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"290 1","pages":"Article 111199"},"PeriodicalIF":1.6000,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Curvature pinching estimate under the Laplacian G2 flow\",\"authors\":\"Chuanhuan Li , Yi Li\",\"doi\":\"10.1016/j.jfa.2025.111199\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we derive a pinching estimate for the traceless Ricci curvature in terms of scalar curvature and the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor under the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow for closed <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> structures. Then we apply this estimate to study the long time existence of the Laplacian <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> flow and prove that the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"290 1\",\"pages\":\"Article 111199\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2025-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123625003817\",\"RegionNum\":2,\"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":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123625003817","RegionNum":2,"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

摘要

本文用标量曲率和闭G2结构下Laplacian G2流下Weyl张量的C1范数，导出了无迹Ricci曲率的捏缩估计。然后应用这一估计研究了拉普拉斯G2流的长时间存在性，证明了Weyl张量的C1范数在有界标量曲率下必须至少以一定的速率爆炸。

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

Curvature pinching estimate under the Laplacian G2 flow

In this paper, we derive a pinching estimate for the traceless Ricci curvature in terms of scalar curvature and the

C^{1}

norm of the Weyl tensor under the Laplacian

G_{2}

flow for closed

G_{2}

structures. Then we apply this estimate to study the long time existence of the Laplacian

G_{2}

flow and prove that the

C^{1}

norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.

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

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis