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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:

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  • Filling radius
  • Филинг-радиус
  • Філінг-радіус
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  • 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:
  • Филинг-радиус — метрическая характеристика Риманова многообразия. Предложенa Громовым в 1983 году.Он использовал филинг-радиусв доказательстве для существенных многообразий.
  • Філінг-радіус — метрична характеристика ріманового многовиду. Запропонована Громовим в 1983 році. Він використовував філінг-радіус в доведенні систолічної нерівності для істотних многовидів.
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  • 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:
  • Филинг-радиус — метрическая характеристика Риманова многообразия. Предложенa Громовым в 1983 году.Он использовал филинг-радиусв доказательстве для существенных многообразий.
  • Філінг-радіус — метрична характеристика ріманового многовиду. Запропонована Громовим в 1983 році. Він використовував філінг-радіус в доведенні систолічної нерівності для істотних многовидів.
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