Acta Mathematica Sinica, English Series

, Volume 35, Issue 7, pp 1217–1226 | Cite as

Gradient Estimates and Harnack Inequalities for Positive Solutions of \(\mathfrak{L}u=\frac{\partial u}{\partial t}\) on Self-shrinkers

  • Ye Cheng ZhuEmail author
  • Qing ChenEmail author


In this paper, we investigate the positive solutions of \(\mathfrak{L}u=\frac{\partial u}{\partial t}\) on self-shrinkers, then get some gradient estimates and Harnack inequalities for the positive solutions.


Harnack inequality self-shrinker ∞-Bakry-Emery Ricci tensor gradient estimate 

MR(2010) Subject Classification

53C23 53C44 


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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsAnhui University of TechnologyMaanshanP. R. China
  2. 2.Department of MathematicsUniversity of Science and Technology of ChinaHefeiP. R. China

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