ricci-bourguignon流非线性后向热方程的哈纳克估计

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of the Korean Mathematical Society Pub Date : 2020-01-01 DOI:10.4134/JKMS.J190049

Jian-hong Wang

{"title":"ricci-bourguignon流非线性后向热方程的哈纳克估计","authors":"Jian-hong Wang","doi":"10.4134/JKMS.J190049","DOIUrl":null,"url":null,"abstract":"In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"313-329"},"PeriodicalIF":0.7000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"HARNACK ESTIMATES FOR NONLINEAR BACKWARD HEAT EQUATIONS WITH POTENTIALS ALONG THE RICCI-BOURGUIGNON FLOW\",\"authors\":\"Jian-hong Wang\",\"doi\":\"10.4134/JKMS.J190049\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.\",\"PeriodicalId\":49993,\"journal\":{\"name\":\"Journal of the Korean Mathematical Society\",\"volume\":\"57 1\",\"pages\":\"313-329\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/JKMS.J190049\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J190049","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文给出了Ricci- bourguignon流耦合的闭流形非线性后向热型方程正解的各种微分哈纳克估计，这是J.-Y对Ricci流所做的。吴[30]。这个证明完全遵循x - d给出的证明。Cao[4]为与Ricci流耦合的线性后向热型方程。

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

HARNACK ESTIMATES FOR NONLINEAR BACKWARD HEAT EQUATIONS WITH POTENTIALS ALONG THE RICCI-BOURGUIGNON FLOW

In this paper, we derive various differential Harnack estimates for positive solutions to the nonlinear backward heat type equations on closed manifolds coupled with the Ricci-Bourguignon flow, which was done for the Ricci flow by J.-Y. Wu [30]. The proof follows exactly the one given by X.-D. Cao [4] for the linear backward heat type equations coupled with the Ricci flow.

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 the Korean Mathematical Society 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).