Ridges in Euclidean Geometry

Abstract

We now take a closer look at the definition for local extrema of a function f ∈ C ^2(ℝ^ n , ℝ). Ridges will be a generalization of local maxima whereby the test for maximality of f ( x ) is made in a restricted neighborhood of x . A similar concept of courses generalizes local minima, but since local minima of f are local maxima of — f , it is sufficient to study only the concept of ridge.