STABILITY





Definition


    

  1. A harmonic morphism f:(M^m,g)--->(N^n,h) between two Riemannian manifolds
is called stable (energy-stable) if the second variation of the energy is
non-negative for any smooth variation f_{t} of f=f_{0}. Unstable otherwise.
    


  2. A manifold (M^m,g) is called stable (unstable) if the identity map 
is stable (unstable).
    





General Stability

Composition

Minimising properties