Evolution of a geometric constant along the Ricci flow

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• 作者：Guangyue Huang ; Zhi Li
• 关键词：58C40 ; 53C44 ; Ricci flow ; normalized Ricci flow ; conjugate heat equation
• 刊名：Journal of Inequalities and Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,301 KB
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  8. Guo, H, Ishida, M: Harnack estimates for nonlinear heat equations with potentials in geometric flows. Manuscr. Math. 148, 471-484 (2015) CrossRef MathSciNet
  
• 作者单位：Guangyue Huang (1)
  Zhi Li (1)
  
  1. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, People’s Republic of China
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

In this paper, we establish the first variation formula of the lowest constant \(\lambda_{a}^{b}(g)\) along the Ricci flow and the normalized Ricci flow, such that to the following nonlinear equation there exist positive solutions: $$-\Delta u+au\log u+bRu=\lambda_{a}^{b} u $$