Cut Locus (Riemannian Manifold)

Cut Locus (Riemannian Manifold)

In Riemannian geometry, the cut locus of a point in a manifold is roughly the set of all other points for which there are multiple minimizing geodesics connecting them from, but it may contain additional points where the minimizing geodesic is unique, under certain circumstances. The distance function from p is a smooth function except at the point p itself and the cut locus.

Read more about Cut Locus (Riemannian Manifold):  Definition, Characterization, Examples, Applications, Cut Locus of A Subset

Famous quotes containing the words cut and/or locus:

    ...there is hope for a tree, if it is cut down, that it will sprout again, and that its shoots will not cease. Though its root grows old in the earth, and its stump dies in the ground, yet at the scent of water it will bud and put forth branches like a young plant. But mortals die, and are laid low; humans expire, and where are they?
    Bible: Hebrew, Job 14:7-10.

    Seeing the locus of joy as the gate
    of a city, or as a lych-gate ...
    Denise Levertov (b. 1923)