For a real valued smooth function on a Riemannian manifold by "gradient extremal set" we mean all critical points of the restriction to the fiber of the square of norm of the gradient. For a generic (Morse) function this is set is a union of smooth curves which intersect "transversally" at critical points. A part of the gradient extremal set gradient which correspond to the local minima is call a "Talweg" or "ridge and valley lines". It can be used to estimate the length of gradient trajectories and possibly should organise dynamics of the gradient flow.