##  [Calabi Flow](/calabi-flow) 

  ##  [Calabi Flow](https://puremath.quantumdictionary.io/calabi-flow-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A parabolic evolution of Kähler metrics within a fixed Kähler class driven by the gradient of the Calabi energy (the L2-norm of scalar curvature), intended to decrease the Calabi functional and approach extremal Kähler metrics; typically a fourth-order geometric PDE when written in potentials.