##  [Harmonic Map Heat Flow](/index.php/harmonic-map-heat-flow) 

  ##  [Harmonic Map Heat Flow](https://puremath.quantumdictionary.io/harmonic-map-heat-flow-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The gradient flow of the Dirichlet energy for a map between Riemannian manifolds: the map evolves by a parabolic PDE (the heat flow) that decreases energy and, when it converges, produces harmonic maps as steady states; also called harmonic map flow or heat flow for harmonic maps.