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山东大学学报(理学版) ›› 2017, Vol. 52 ›› Issue (4): 83-86.doi: 10.6040/j.issn.1671-9352.0.2016.364

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f-调和函数的Hess矩阵的估计及其在分裂定理中的应用

邓义华   

  1. 衡阳师范学院数学与统计学院, 湖南 衡阳 421002
  • 收稿日期:2016-07-23 出版日期:2017-04-20 发布日期:2017-04-11
  • 作者简介:邓义华(1971— ),男,硕士,教授,研究方向为微分几何与微分方程. E-mail:dengchen4032@126.com
  • 基金资助:
    湖南省教育厅重点项目(14A020);湖南省自然科学基金项目(14JJ2120);湖南省重点建设学科资助

Estimates for the Hessian of f-harmonic functions and their applications to splitting theorem

DENG Yi-hua   

  1. College of Mathematics and Statistics, Hengyang Normal University, Hengyang 421002, Hunan, China
  • Received:2016-07-23 Online:2017-04-20 Published:2017-04-11

摘要: 得到了f-调和函数的Hess矩阵的一个新的估计。 运用这个新的估计,对具有加权Poincaré不等式以及Bakry-Émery Ricci曲率的下界是负函数的光滑度量测度空间上的一个分裂定理进行了改进。

关键词: 加权Poincaré 不等式, 光滑度量测度空间, f-调和函数, 分裂定理

Abstract: A new estimate for the Hessian of f-harmonic functions is obtained. Using the new estimate, we improve a splitting theorem on smooth metric measure space with weighted Poincaré inequality under the condition that the Bakry-Émery Ricci curvature is bounded from below by some negative functions.

Key words: smooth metric measure spaces, splitting theorem, weighted Poincaré inequality, f-harmonic function

中图分类号: 

  • O186.16
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