isoperimetric defect

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• Defect — Defect, defects, or defected may refer to: Geometry and physical sciences Defect (geometry), a characteristic of a polyhedron Topological defect Isoperimetric defect Crystallographic defect, a structural imperfection in a crystal Biology and… …   Wikipedia

• Introduction to systolic geometry — Systolic geometry is a branch of differential geometry, a field within mathematics, studying problems such as the relationship between the area inside a closed curve C , and the length or perimeter of C . Since the area A may be small while the… …   Wikipedia

• Systolic geometry — In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner, and developed by Mikhail Gromov and others, in its arithmetic, ergodic, and topological manifestations.… …   Wikipedia

• Bonnesen's inequality — is an inequality relating the length, the area, the radius of the incircle and the radius of the circumcircle of a Jordan curve. It is a strengthening of the classical isoperimetric inequality.More precisely, consider a planar simple closed curve …   Wikipedia

• Loewner's torus inequality — In differential geometry, Loewner s torus inequality is an inequality due to Charles Loewner for the systole of an arbitrary Riemannian metric on the 2 torus.tatementIn 1949 Charles Loewner proved that every metric on the 2 torus mathbb T^2… …   Wikipedia

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