In Riemannian geometry, the filling radius of a Riemannian manifold X is a metric invariant of X. It was originally introduced in 1983 by Mikhail Gromov, who used it to prove his systolic inequality for essential manifolds, vastly generalizing Loewner's torus inequality and Pu's inequality for the real projective plane, and creating Systolic geometry in its modern form.
The filling radius of a simple loop C in the plane is defined as the largest radius, R>0, of a circle that fits inside C:
Read more about Filling Radius: Dual Definition Via Neighborhoods, Homological Definition, Relation To Diameter and Systole
Famous quotes containing the word filling:
“Science has done great things for us; it has also pushed us hopelessly back. For, not content with filling its own place, it has tried to supersede everything else. It has challenged the super-eminence of religion; it has turned all philosophy out of doors except that which clings to its skirts; it has thrown contempt on all learning that does not depend on it; and it has bribed the skeptics by giving us immense material comforts.”
—Katharine Fullerton Gerould (1879–1944)