{"title":"An improved Hamilton matrix estimates for the heat equation","authors":"Lang Qin, Qi S. Zhang","doi":"arxiv-2409.10379","DOIUrl":null,"url":null,"abstract":"In this paper, we remove the assumption on the gradient of the Ricci\ncurvature in Hamilton's matrix Harnack estimate for the heat equation on all\nclosed manifolds, answering a question which has been around since the 1990s.\nNew ingredients include a recent sharp Li-Yau estimate, construction of a\nsuitable vector field and various use of integral arguments, iteration and a\nlittle tensor algebra.","PeriodicalId":501113,"journal":{"name":"arXiv - MATH - Differential Geometry","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10379","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we remove the assumption on the gradient of the Ricci
curvature in Hamilton's matrix Harnack estimate for the heat equation on all
closed manifolds, answering a question which has been around since the 1990s.
New ingredients include a recent sharp Li-Yau estimate, construction of a
suitable vector field and various use of integral arguments, iteration and a
little tensor algebra.
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