Potential Analysis

, Volume 25, Issue 4, pp 399–406 | Cite as

Bakry–Emery Curvature Operator and Ricci Flow

  • Qi-hua Ruan


In this paper, we introduce some techniques of Bakry–Emery curvature operator to Ricci flow and prove the evolution equation for the Bakry–Emery scalar curvature. As its application, we can easily derive the Perelman’s entropy functional monotonicity formula. We also discuss some gradient estimates of Ricci curvature and L 2– estimates of scalar curvature.

Key words

Bakry–Emery curvature operator Ricci flow gradient estimates 

Mathematics Subject Classifications (2000)

53C20 53C21 


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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.School of MathematicsZhongshan University, GuangzhouGuangdongPeople’s Republic of China
  2. 2.Department of MathematicsPutian University, PutianFujianPeople’s Republic of China

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