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:
“I am filling the room
with the words from my pen.
Words leak out of it like a miscarriage.
I am zinging words out into the air
and they come back like squash balls.
Yet there is silence.”
—Anne Sexton (1928–1974)