Riemannian geometry | Differential geometry | Systolic geometry

Filling radius

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: (Wikipedia).

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Related pages

Kuratowski embedding | Pu's inequality | Real projective space | Gromov's systolic inequality for essential manifolds | Systolic geometry | Riemannian manifold | Fundamental class | Filling area conjecture | Riemannian geometry | Loewner's torus inequality | Essential manifold